Abstract
We introduce the extension of local polynomial fitting to the linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to nonparametric technique of local polynomial estimation, we do not need to know the heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we focus on comparison of parameters and reach an optimal fitting. Besides, we verify the asymptotic normality of parameters based on numerical simulations. Finally, this approach is applied to a case of economics, and it indicates that our method is surely effective in finite-sample situations.
Highlights
The heteroscedasticity in classical linear regression model is defined by the variances of random items which are not the same for different explanatory variables and observations
In this paper we presented a new method for estimation of linear heteroscedastic regression model based on local polynomial estimation with nonparametric technique
The proposed scheme firstly adopted the local polynomial fitting to estimate heteroscedastic function, the coefficients of regression model are obtained based on generalized least squares method
Summary
The heteroscedasticity in classical linear regression model is defined by the variances of random items which are not the same for different explanatory variables and observations. In order to solve the problem above, we can use generalized least squares estimation GLS when the covariance matrix of the random items is known If it is unknown, we usually use two-stage least squares estimate, that is, we first estimate variances of the residual error, and the generalized least squares estimator is used to obtain the coefficients of the model by using the estimate of variances of the random items 11, 12. We try to applying local polynomial fitting to random item variances as the first step, and GLS is used to estimate the coefficients of the model.
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