Search results for: maximum likelihood estimation method
9852 On Best Estimation for Parameter Weibull Distribution
Authors: Hadeel Salim Alkutubi
Abstract:
The objective of this study is to introduce estimators to the parameters and survival function for Weibull distribution using three different methods, Maximum Likelihood estimation, Standard Bayes estimation and Modified Bayes estimation. We will then compared the three methods using simulation study to find the best one base on MPE and MSE.
Keywords: Maximum Likelihood estimation , Bayes estimation, Jeffery prior information, Simulation study
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12519851 Contour Estimation in Synthetic and Real Weld Defect Images based on Maximum Likelihood
Authors: M. Tridi, N. Nacereddine, N. Oucief
Abstract:
This paper describes a novel method for automatic estimation of the contours of weld defect in radiography images. Generally, the contour detection is the first operation which we apply in the visual recognition system. Our approach can be described as a region based maximum likelihood formulation of parametric deformable contours. This formulation provides robustness against the poor image quality, and allows simultaneous estimation of the contour parameters together with other parameters of the model. Implementation is performed by a deterministic iterative algorithm with minimal user intervention. Results testify for the very good performance of the approach especially in synthetic weld defect images.Keywords: Contour, gaussian, likelihood, rayleigh.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16479850 Parameter Estimation using Maximum Likelihood Method from Flight Data at High Angles of Attack
Authors: Rakesh Kumar, A. K. Ghosh
Abstract:
The paper presents the modeling of nonlinear longitudinal aerodynamics using flight data of Hansa-3 aircraft at high angles of attack near stall. The Kirchhoff-s quasi-steady stall model has been used to incorporate nonlinear aerodynamic effects in the aerodynamic model used to estimate the parameters, thereby, making the aerodynamic model nonlinear. The Maximum Likelihood method has been applied to the flight data (at high angles of attack) for the estimation of parameters (aerodynamic and stall characteristics) using the nonlinear aerodynamic model. To improve the accuracy level of the estimates, an approach of fixing the strong parameters has also been presented.Keywords: Maximum Likelihood, nonlinear, parameters, stall.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22009849 Estimating Regression Effects in Com Poisson Generalized Linear Model
Authors: Vandna Jowaheer, Naushad A. Mamode Khan
Abstract:
Com Poisson distribution is capable of modeling the count responses irrespective of their mean variance relation and the parameters of this distribution when fitted to a simple cross sectional data can be efficiently estimated using maximum likelihood (ML) method. In the regression setup, however, ML estimation of the parameters of the Com Poisson based generalized linear model is computationally intensive. In this paper, we propose to use quasilikelihood (QL) approach to estimate the effect of the covariates on the Com Poisson counts and investigate the performance of this method with respect to the ML method. QL estimates are consistent and almost as efficient as ML estimates. The simulation studies show that the efficiency loss in the estimation of all the parameters using QL approach as compared to ML approach is quite negligible, whereas QL approach is lesser involving than ML approach.
Keywords: Com Poisson, Cross-sectional, Maximum Likelihood, Quasi likelihood
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17509848 Bootstrap Confidence Intervals and Parameter Estimation for Zero Inflated Strict Arcsine Model
Authors: Y. N. Phang, E. F. Loh
Abstract:
Zero inflated Strict Arcsine model is a newly developed model which is found to be appropriate in modeling overdispersed count data. In this study, maximum likelihood estimation method is used in estimating the parameters for zero inflated strict arcsine model. Bootstrapping is then employed to compute the confidence intervals for the estimated parameters.
Keywords: overdispersed count data, maximum likelihood estimation, simulated annealing, BCa confidence intervals.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22709847 Frequency Estimation Using Analytic Signal via Wavelet Transform
Authors: Sudipta Majumdar, Akansha Singh
Abstract:
Frequency estimation of a sinusoid in white noise using maximum entropy power spectral estimation has been shown to be very sensitive to initial sinusoidal phase. This paper presents use of wavelet transform to find an analytic signal for frequency estimation using maximum entropy method (MEM) and compared the results with frequency estimation using analytic signal by Hilbert transform method and frequency estimation using real data together with MEM. The presented method shows the improved estimation precision and antinoise performance.Keywords: Frequency estimation, analytic signal, maximum entropy method, wavelet transform.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17289846 Maximum Likelihood Estimation of Burr Type V Distribution under Left Censored Samples
Abstract:
The paper deals with the maximum likelihood estimation of the parameters of the Burr type V distribution based on left censored samples. The maximum likelihood estimators (MLE) of the parameters have been derived and the Fisher information matrix for the parameters of the said distribution has been obtained explicitly. The confidence intervals for the parameters have also been discussed. A simulation study has been conducted to investigate the performance of the point and interval estimates.
Keywords: Fisher information matrix, confidence intervals, censoring.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16949845 Frequency Offset Estimation Schemes Based On ML for OFDM Systems in Non-Gaussian Noise Environments
Authors: Keunhong Chae, Seokho Yoon
Abstract:
In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.
Keywords: Frequency offset estimation, maximum-likelihood, non-Gaussian noise environment, OFDM, training symbol.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19369844 ML-Based Blind Frequency Offset Estimation Schemes for OFDM Systems in Non-Gaussian Noise Environments
Authors: Keunhong Chae, Seokho Yoon
Abstract:
This paper proposes frequency offset (FO) estimation schemes robust to the non-Gaussian noise for orthogonal frequency division multiplexing (OFDM) systems. A maximum-likelihood (ML) scheme and a low-complexity estimation scheme are proposed by applying the probability density function of the cyclic prefix of OFDM symbols to the ML criterion. From simulation results, it is confirmed that the proposed schemes offer a significant FO estimation performance improvement over the conventional estimation scheme in non-Gaussian noise environments.
Keywords: Frequency offset, cyclic prefix, maximum-likelihood, non-Gaussian noise, OFDM.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20099843 An Estimating Parameter of the Mean in Normal Distribution by Maximum Likelihood, Bayes, and Markov Chain Monte Carlo Methods
Authors: Autcha Araveeporn
Abstract:
This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.
Keywords: Bayes method, Markov Chain Monte Carlo method, Maximum Likelihood method, normal distribution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14179842 Zero Truncated Strict Arcsine Model
Authors: Y. N. Phang, E. F. Loh
Abstract:
The zero truncated model is usually used in modeling count data without zero. It is the opposite of zero inflated model. Zero truncated Poisson and zero truncated negative binomial models are discussed and used by some researchers in analyzing the abundance of rare species and hospital stay. Zero truncated models are used as the base in developing hurdle models. In this study, we developed a new model, the zero truncated strict arcsine model, which can be used as an alternative model in modeling count data without zero and with extra variation. Two simulated and one real life data sets are used and fitted into this developed model. The results show that the model provides a good fit to the data. Maximum likelihood estimation method is used in estimating the parameters.
Keywords: Hurdle models, maximum likelihood estimation method, positive count data.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18419841 Exponentiated Transmuted Weibull Distribution A Generalization of the Weibull Distribution
Authors: Abd El Hady N. Ebraheim
Abstract:
This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.
Keywords: Exponentiated, Inversion Method, Maximum Likelihood Estimation, Transmutation Map.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 34529840 Inferences on Compound Rayleigh Parameters with Progressively Type-II Censored Samples
Authors: Abdullah Y. Al-Hossain
Abstract:
This paper considers inference under progressive type II censoring with a compound Rayleigh failure time distribution. The maximum likelihood (ML), and Bayes methods are used for estimating the unknown parameters as well as some lifetime parameters, namely reliability and hazard functions. We obtained Bayes estimators using the conjugate priors for two shape and scale parameters. When the two parameters are unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We use Lindley.s approximation to compute the Bayes estimates. Another Bayes estimator has been obtained based on continuous-discrete joint prior for the unknown parameters. An example with the real data is discussed to illustrate the proposed method. Finally, we made comparisons between these estimators and the maximum likelihood estimators using a Monte Carlo simulation study.
Keywords: Progressive type II censoring, compound Rayleigh failure time distribution, maximum likelihood estimation, Bayes estimation, Lindley's approximation method, Monte Carlo simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23749839 Bayesian Inference for Phase Unwrapping Using Conjugate Gradient Method in One and Two Dimensions
Authors: Yohei Saika, Hiroki Sakaematsu, Shota Akiyama
Abstract:
We investigated statistical performance of Bayesian inference using maximum entropy and MAP estimation for several models which approximated wave-fronts in remote sensing using SAR interferometry. Using Monte Carlo simulation for a set of wave-fronts generated by assumed true prior, we found that the method of maximum entropy realized the optimal performance around the Bayes-optimal conditions by using model of the true prior and the likelihood representing optical measurement due to the interferometer. Also, we found that the MAP estimation regarded as a deterministic limit of maximum entropy almost achieved the same performance as the Bayes-optimal solution for the set of wave-fronts. Then, we clarified that the MAP estimation perfectly carried out phase unwrapping without using prior information, and also that the MAP estimation realized accurate phase unwrapping using conjugate gradient (CG) method, if we assumed the model of the true prior appropriately.
Keywords: Bayesian inference using maximum entropy, MAP estimation using conjugate gradient method, SAR interferometry.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17359838 Modelling Hydrological Time Series Using Wakeby Distribution
Authors: Ilaria Lucrezia Amerise
Abstract:
The statistical modelling of precipitation data for a given portion of territory is fundamental for the monitoring of climatic conditions and for Hydrogeological Management Plans (HMP). This modelling is rendered particularly complex by the changes taking place in the frequency and intensity of precipitation, presumably to be attributed to the global climate change. This paper applies the Wakeby distribution (with 5 parameters) as a theoretical reference model. The number and the quality of the parameters indicate that this distribution may be the appropriate choice for the interpolations of the hydrological variables and, moreover, the Wakeby is particularly suitable for describing phenomena producing heavy tails. The proposed estimation methods for determining the value of the Wakeby parameters are the same as those used for density functions with heavy tails. The commonly used procedure is the classic method of moments weighed with probabilities (probability weighted moments, PWM) although this has often shown difficulty of convergence, or rather, convergence to a configuration of inappropriate parameters. In this paper, we analyze the problem of the likelihood estimation of a random variable expressed through its quantile function. The method of maximum likelihood, in this case, is more demanding than in the situations of more usual estimation. The reasons for this lie, in the sampling and asymptotic properties of the estimators of maximum likelihood which improve the estimates obtained with indications of their variability and, therefore, their accuracy and reliability. These features are highly appreciated in contexts where poor decisions, attributable to an inefficient or incomplete information base, can cause serious damages.Keywords: Generalized extreme values (GEV), likelihood estimation, precipitation data, Wakeby distribution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6529837 Zero Inflated Strict Arcsine Regression Model
Authors: Y. N. Phang, E. F. Loh
Abstract:
Zero inflated strict arcsine model is a newly developed model which is found to be appropriate in modeling overdispersed count data. In this study, we extend zero inflated strict arcsine model to zero inflated strict arcsine regression model by taking into consideration the extra variability caused by extra zeros and covariates in count data. Maximum likelihood estimation method is used in estimating the parameters for this zero inflated strict arcsine regression model.Keywords: Overdispersed count data, maximum likelihood estimation, simulated annealing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17409836 Forecasting the Volatility of Geophysical Time Series with Stochastic Volatility Models
Authors: Maria C. Mariani, Md Al Masum Bhuiyan, Osei K. Tweneboah, Hector G. Huizar
Abstract:
This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.Keywords: Augmented Dickey Fuller Test, geophysical time series, maximum likelihood estimation, stochastic volatility model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8499835 Estimation of R= P [Y < X] for Two-parameter Burr Type XII Distribution
Abstract:
In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The exact confidence interval of the R is also obtained. Monte Carlo simulations are performed to compare the different proposed methods.
Keywords: Stress-Strength model, Maximum likelihood estimator, Bayes estimator, Burr type XII distribution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22719834 Automatic Detection of Mass Type Breast Cancer using Texture Analysis in Korean Digital Mammography
Authors: E. B. Jo, J. H. Lee, J. Y. Park, S. M. Kim
Abstract:
In this study, we present an advanced detection technique for mass type breast cancer based on texture information of organs. The proposed method detects the cancer areas in three stages. In the first stage, the midpoints of mass area are determined based on AHE (Adaptive Histogram Equalization). In the second stage, we set the threshold coefficient of homogeneity by using MLE (Maximum Likelihood Estimation) to compute the uniformity of texture. Finally, mass type cancer tissues are extracted from the original image. As a result, it was observed that the proposed method shows an improved detection performance on dense breast tissues of Korean women compared with the existing methods. It is expected that the proposed method may provide additional diagnostic information for detection of mass-type breast cancer.Keywords: Mass Type Breast Cancer, Mammography, Maximum Likelihood Estimation (MLE), Ranklets, SVM
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19719833 A Novel Estimation Method for Integer Frequency Offset in Wireless OFDM Systems
Authors: Taeung Yoon, Youngpo Lee, Chonghan Song, Na Young Ha, Seokho Yoon
Abstract:
Ren et al. presented an efficient carrier frequency offset (CFO) estimation method for orthogonal frequency division multiplexing (OFDM), which has an estimation range as large as the bandwidth of the OFDM signal and achieves high accuracy without any constraint on the structure of the training sequence. However, its detection probability of the integer frequency offset (IFO) rapidly varies according to the fractional frequency offset (FFO) change. In this paper, we first analyze the Ren-s method and define two criteria suitable for detection of IFO. Then, we propose a novel method for the IFO estimation based on the maximum-likelihood (ML) principle and the detection criteria defined in this paper. The simulation results demonstrate that the proposed method outperforms the Ren-s method in terms of the IFO detection probability irrespective of a value of the FFO.Keywords: Orthogonal frequency division multiplexing, integer frequency offset, estimation, training symbol
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24409832 Hazard Rate Estimation of Temporal Point Process, Case Study: Earthquake Hazard Rate in Nusatenggara Region
Authors: Sunusi N., Kresna A. J., Islamiyati A., Raupong
Abstract:
Hazard rate estimation is one of the important topics in forecasting earthquake occurrence. Forecasting earthquake occurrence is a part of the statistical seismology where the main subject is the point process. Generally, earthquake hazard rate is estimated based on the point process likelihood equation called the Hazard Rate Likelihood of Point Process (HRLPP). In this research, we have developed estimation method, that is hazard rate single decrement HRSD. This method was adapted from estimation method in actuarial studies. Here, one individual associated with an earthquake with inter event time is exponentially distributed. The information of epicenter and time of earthquake occurrence are used to estimate hazard rate. At the end, a case study of earthquake hazard rate will be given. Furthermore, we compare the hazard rate between HRLPP and HRSD method.Keywords: Earthquake forecast, Hazard Rate, Likelihood point process, Point process.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14759831 Alternative Robust Estimators for the Shape Parameters of the Burr XII Distribution
Authors: F. Z. Doğru, O. Arslan
Abstract:
In general, classical methods such as maximum likelihood (ML) and least squares (LS) estimation methods are used to estimate the shape parameters of the Burr XII distribution. However, these estimators are very sensitive to the outliers. To overcome this problem we propose alternative robust estimators based on the M-estimation method for the shape parameters of the Burr XII distribution. We provide a small simulation study and a real data example to illustrate the performance of the proposed estimators over the ML and the LS estimators. The simulation results show that the proposed robust estimators generally outperform the classical estimators in terms of bias and root mean square errors when there are outliers in data.
Keywords: Burr XII distribution, robust estimator, M-estimator, maximum likelihood, least squares.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26489830 Likelihood Estimation for Stochastic Epidemics with Heterogeneous Mixing Populations
Authors: Yilun Shang
Abstract:
We consider a heterogeneously mixing SIR stochastic epidemic process in populations described by a general graph. Likelihood theory is developed to facilitate statistic inference for the parameters of the model under complete observation. We show that these estimators are asymptotically Gaussian unbiased estimates by using a martingale central limit theorem.Keywords: statistic inference, maximum likelihood, epidemicmodel, heterogeneous mixing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13979829 A New Distribution and Application on the Lifetime Data
Authors: Gamze Ozel, Selen Cakmakyapan
Abstract:
We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study.
Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13779828 Improvement of MLLR Speaker Adaptation Using a Novel Method
Authors: Ing-Jr Ding
Abstract:
This paper presents a technical speaker adaptation method called WMLLR, which is based on maximum likelihood linear regression (MLLR). In MLLR, a linear regression-based transform which adapted the HMM mean vectors was calculated to maximize the likelihood of adaptation data. In this paper, the prior knowledge of the initial model is adequately incorporated into the adaptation. A series of speaker adaptation experiments are carried out at a 30 famous city names database to investigate the efficiency of the proposed method. Experimental results show that the WMLLR method outperforms the conventional MLLR method, especially when only few utterances from a new speaker are available for adaptation.Keywords: hidden Markov model, maximum likelihood linearregression, speech recognition, speaker adaptation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18329827 ML Detection with Symbol Estimation for Nonlinear Distortion of OFDM Signal
Authors: Somkiat Lerkvaranyu, Yoshikazu Miyanaga
Abstract:
In this paper, a new technique of signal detection has been proposed for detecting the orthogonal frequency-division multiplexing (OFDM) signal in the presence of nonlinear distortion.There are several advantages of OFDM communications system.However, one of the existing problems is remain considered as the nonlinear distortion generated by high-power-amplifier at the transmitter end due to the large dynamic range of an OFDM signal. The proposed method is the maximum likelihood detection with the symbol estimation. When the training data are available, the neural network has been used to learn the characteristic of received signal and to estimate the new positions of the transmitted symbol which are provided to the maximum likelihood detector. Resulting in the system performance, the nonlinear distortions of a traveling wave tube amplifier with OFDM signal are considered in this paper.Simulation results of the bit-error-rate performance are obtained with 16-QAM OFDM systems.
Keywords: OFDM, TWTA, nonlinear distortion, detection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16629826 Comparison of Methods of Estimation for Use in Goodness of Fit Tests for Binary Multilevel Models
Authors: I. V. Pinto, M. R. Sooriyarachchi
Abstract:
It can be frequently observed that the data arising in our environment have a hierarchical or a nested structure attached with the data. Multilevel modelling is a modern approach to handle this kind of data. When multilevel modelling is combined with a binary response, the estimation methods get complex in nature and the usual techniques are derived from quasi-likelihood method. The estimation methods which are compared in this study are, marginal quasi-likelihood (order 1 & order 2) (MQL1, MQL2) and penalized quasi-likelihood (order 1 & order 2) (PQL1, PQL2). A statistical model is of no use if it does not reflect the given dataset. Therefore, checking the adequacy of the fitted model through a goodness-of-fit (GOF) test is an essential stage in any modelling procedure. However, prior to usage, it is also equally important to confirm that the GOF test performs well and is suitable for the given model. This study assesses the suitability of the GOF test developed for binary response multilevel models with respect to the method used in model estimation. An extensive set of simulations was conducted using MLwiN (v 2.19) with varying number of clusters, cluster sizes and intra cluster correlations. The test maintained the desirable Type-I error for models estimated using PQL2 and it failed for almost all the combinations of MQL. Power of the test was adequate for most of the combinations in all estimation methods except MQL1. Moreover, models were fitted using the four methods to a real-life dataset and performance of the test was compared for each model.
Keywords: Goodness-of-fit test, marginal quasi-likelihood, multilevel modelling, type-I error, penalized quasi-likelihood, power, quasi-likelihood.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7239825 The Maximum Likelihood Method of Random Coefficient Dynamic Regression Model
Authors: Autcha Araveeporn
Abstract:
The Random Coefficient Dynamic Regression (RCDR) model is to developed from Random Coefficient Autoregressive (RCA) model and Autoregressive (AR) model. The RCDR model is considered by adding exogenous variables to RCA model. In this paper, the concept of the Maximum Likelihood (ML) method is used to estimate the parameter of RCDR(1,1) model. Simulation results have shown the AIC and BIC criterion to compare the performance of the the RCDR(1,1) model. The variables as the stationary and weakly stationary data are good estimates where the exogenous variables are weakly stationary. However, the model selection indicated that variables are nonstationarity data based on the stationary data of the exogenous variables.Keywords: Autoregressive, Maximum Likelihood Method, Nonstationarity, Random Coefficient Dynamic Regression, Stationary.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16359824 A Rule-based Approach for Anomaly Detection in Subscriber Usage Pattern
Authors: Rupesh K. Gopal, Saroj K. Meher
Abstract:
In this report we present a rule-based approach to detect anomalous telephone calls. The method described here uses subscriber usage CDR (call detail record) data sampled over two observation periods: study period and test period. The study period contains call records of customers- non-anomalous behaviour. Customers are first grouped according to their similar usage behaviour (like, average number of local calls per week, etc). For customers in each group, we develop a probabilistic model to describe their usage. Next, we use maximum likelihood estimation (MLE) to estimate the parameters of the calling behaviour. Then we determine thresholds by calculating acceptable change within a group. MLE is used on the data in the test period to estimate the parameters of the calling behaviour. These parameters are compared against thresholds. Any deviation beyond the threshold is used to raise an alarm. This method has the advantage of identifying local anomalies as compared to techniques which identify global anomalies. The method is tested for 90 days of study data and 10 days of test data of telecom customers. For medium to large deviations in the data in test window, the method is able to identify 90% of anomalous usage with less than 1% false alarm rate.Keywords: Subscription fraud, fraud detection, anomalydetection, maximum likelihood estimation, rule based systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27989823 Numerical Optimization within Vector of Parameters Estimation in Volatility Models
Authors: J. Arneric, A. Rozga
Abstract:
In this paper usefulness of quasi-Newton iteration procedure in parameters estimation of the conditional variance equation within BHHH algorithm is presented. Analytical solution of maximization of the likelihood function using first and second derivatives is too complex when the variance is time-varying. The advantage of BHHH algorithm in comparison to the other optimization algorithms is that requires no third derivatives with assured convergence. To simplify optimization procedure BHHH algorithm uses the approximation of the matrix of second derivatives according to information identity. However, parameters estimation in a/symmetric GARCH(1,1) model assuming normal distribution of returns is not that simple, i.e. it is difficult to solve it analytically. Maximum of the likelihood function can be founded by iteration procedure until no further increase can be found. Because the solutions of the numerical optimization are very sensitive to the initial values, GARCH(1,1) model starting parameters are defined. The number of iterations can be reduced using starting values close to the global maximum. Optimization procedure will be illustrated in framework of modeling volatility on daily basis of the most liquid stocks on Croatian capital market: Podravka stocks (food industry), Petrokemija stocks (fertilizer industry) and Ericsson Nikola Tesla stocks (information-s-communications industry).Keywords: Heteroscedasticity, Log-likelihood Maximization, Quasi-Newton iteration procedure, Volatility.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2633