Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33063
The Profit Trend of Cosmetics Products Using Bootstrap Edgeworth Approximation
Authors: Edlira Donefski, Lorenc Ekonomi, Tina Donefski
Abstract:
Edgeworth approximation is one of the most important statistical methods that has a considered contribution in the reduction of the sum of standard deviation of the independent variables’ coefficients in a Quantile Regression Model. This model estimates the conditional median or other quantiles. In this paper, we have applied approximating statistical methods in an economical problem. We have created and generated a quantile regression model to see how the profit gained is connected with the realized sales of the cosmetic products in a real data, taken from a local business. The Linear Regression of the generated profit and the realized sales was not free of autocorrelation and heteroscedasticity, so this is the reason that we have used this model instead of Linear Regression. Our aim is to analyze in more details the relation between the variables taken into study: the profit and the finalized sales and how to minimize the standard errors of the independent variable involved in this study, the level of realized sales. The statistical methods that we have applied in our work are Edgeworth Approximation for Independent and Identical distributed (IID) cases, Bootstrap version of the Model and the Edgeworth approximation for Bootstrap Quantile Regression Model. The graphics and the results that we have presented here identify the best approximating model of our study.Keywords: Bootstrap, Edgeworth approximation, independent and Identical distributed, quantile.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 437References:
[1] A. H. Welsh, Asymptotically Efficient Estimation of the Sparsity Function at a Point, Statistics & Probability Letters, 6 (1988), 427-432.
[2] D. A. Bloch and J. L. Gastwirth, On a simple estimate of the reciprocal of the density function, Ann. Math. Statist. 39 (1968), 1083-1085.
[3] G. J. Bassett and R. Koenker, An Empirical Quantile Function for Linear Models with i.i.d. Errors,” Journal of the American Statistical Association, 77(378) (1982), 407-415.
[4] H. A. David, Order Statistics, 2nd ed. Wiley, New York, 1981.
[5] J. Powell, Censored Regression Quantiles, Journal of Econometrics, 32 (1986), 143-155.
[6] M. Buchinsky, Estimating the Asymptotic Covariance Matrix for Quantile Regression Models: A Monte Carlo Study, Journal of Econometrics, 68 (1995), 303-338.
[7] M. C. Jones, Estimating Densities, Quantiles, Quantile Densities and Density Quantiles, Annals of the Institute of Statistical Mathematics, 44(4) (1992), 721-727.
[8] M. Kocherginsky, X. He, and Y. Mu, Practical Confidence Intervals for Regression Quantiles, Journal of Computational and Graphical Statistics, 14(1) (2005), 41-55.
[9] M. M. Siddiqui, Distribution of Quantiles in Samples from a Bivariate Population, Journal of Research of the National Bureau of Standards–B, 64(3) (1960), 145-150.
[10] P. Hall, The Bootstrap and Edgeworth Expansion, Springer-Verlag, New York, USA, 1992.
[11] P. Hall and M. A. Martin, On the error incurred using the bootstrap variance estimate when constructing confidence intervals for quantiles, J. Mult. Anal. 38 (1991). 70-81.
[12] P. Hall and S. J. Sheather, On the Distribution of the Studentized Quantile, Journal of the Royal Statistical Society, Series B, 50(3) (1988), 381-391.
[13] R. Koenker and G.J. Bassett, Regression Quantiles, Econometrica, 46(1) (1978), 33-50.
[14] R. Koenker, P. Mandl and M. Huskova, Confidence Intervals for Regression Quantiles, in Asymptotic Statistics, eds., New York: Springer-Verlag, (1994), 349-359.
[15] X. He and F. Hu, Markov Chain Marginal Bootstrap, Journal of the American Statistical Association, 97(459) (2002), 783-795.
[16] http://www.eviews.com/help/helpintro.html#page/content%2Fquantreg-Background.html%23
[17] https://idoc.pub/documents/eviews-8-users-guide-ii-on2397q8dyl0