Analýza funkčnosti zobecněné metody nejmenších čtverců při odhadu regresních parametrů za podmínek heteroskedasticity

Abstract

Linear regression and single phases of the regression model construction are summarized in the theoretical part. Least squares method and the conditions random part of model which have to be fulfilled to make an accurate estimate using by this method are also described. Next part is devoted to the failure non-compliance one of the conditions – homoscedasticity. Generalized least squares method i sone of the mothod how to solve heteroscedasticity. Variance estimation and measuring the quality of the estimate using the mean square error i salso described in this thesis. Experimental part of the thesis was focused on simulations, in which is investigated when it is better to use the least squares method and when better estimation are reached by generalized least square method. Whole simulation is made in MS Excel, where are tested gradually different settings of parameters Ai, different settings of parameters Bi, different models of variance estimation and different sizes of the number of values in the simulation. The simulation showed that the settings of the parameters Ai, different settings of parameters Bi and the different models of variance estimation do not affect the quality of the parametr estimation. With the set variance the generalized least squares method gives a better estimate of the parameters. However if the variances are estimated then at n=50 the estimation of the parameters was more accurate by the least squares method. In a situation where the variance was estimated again but n= 200 the generalized least squares method gave a more accurate estimate than least squares method.