Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

Median Related Abstracts

3 Median-Based Nonparametric Estimation of Returns in Mean-Downside Risk Portfolio Frontier

Authors: H. Ben Salah, A. Gannoun, C. de Peretti, A. Trabelsi

Abstract:

The Downside Risk (DSR) model for portfolio optimisation allows to overcome the drawbacks of the classical mean-variance model concerning the asymetry of returns and the risk perception of investors. This model optimization deals with a positive definite matrix that is endogenous with respect to portfolio weights. This aspect makes the problem far more difficult to handle. For this purpose, Athayde (2001) developped a new recurcive minimization procedure that ensures the convergence to the solution. However, when a finite number of observations is available, the portfolio frontier presents an appearance which is not very smooth. In order to overcome that, Athayde (2003) proposed a mean kernel estimation of the returns, so as to create a smoother portfolio frontier. This technique provides an effect similar to the case in which we had continuous observations. In this paper, taking advantage on the the robustness of the median, we replace the mean estimator in Athayde's model by a nonparametric median estimator of the returns. Then, we give a new version of the former algorithm (of Athayde (2001, 2003)). We eventually analyse the properties of this improved portfolio frontier and apply this new method on real examples.

Keywords: Downside Risk, Kernel Method, Median, Nonparametric Estimation, Semivariance

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2 Using the Bootstrap for Problems Statistics

Authors: Brahim Boukabcha, Amar Rebbouh

Abstract:

The bootstrap method based on the idea of exploiting all the information provided by the initial sample, allows us to study the properties of estimators. In this article we will present a theoretical study on the different methods of bootstrapping and using the technique of re-sampling in statistics inference to calculate the standard error of means of an estimator and determining a confidence interval for an estimated parameter. We apply these methods tested in the regression models and Pareto model, giving the best approximations.

Keywords: Regression Models, bias, bootstrap, mean, confidence interval, Median, variance, error standard, jackknife

Procedia PDF Downloads 227
1 South African Students' Statistical Literacy in the Conceptual Understanding about Measures of Central Tendency after Completing Their High School Studies

Authors: Lukanda Kalobo

Abstract:

In South Africa, the High School Mathematics Curriculum provides teachers with specific aims and skills to be developed which involves the understanding about the measures of central tendency. The exploration begins with the definitions of statistical literacy, measurement of central tendency and a discussion on why statistical literacy is essential today. It furthermore discusses the statistical literacy basics involved in understanding the concepts of measures of central tendency. The statistical literacy test on the measures of central tendency, was used to collect data which was administered to 78 first year students direct from high schools. The results indicated that students seemed to have forgotten about the statistical literacy in understanding the concepts of measure of central tendency after completing their high school study. The authors present inferences regarding the alignment between statistical literacy and the understanding of the concepts about the measures of central tendency, leading to the conclusion that there is a need to provide in-service and pre-service training.

Keywords: mean, Median, conceptual understanding, mode, statistical literacy

Procedia PDF Downloads 148