scholarly journals Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Liyun Su ◽  
Yanyong Zhao ◽  
Tianshun Yan
Keyword(s):  
Regression Model ◽  
Least Squares Method ◽  
Generalized Least Squares ◽  
Finite Sample ◽  
Local Polynomial Fitting ◽  
Polynomial Fitting ◽  
Two Stage ◽  
Local Polynomial ◽  
Heteroscedastic Regression ◽  
Local Polynomial Estimation

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.

Two-Stage Local Polynomial Regression Method for Image Heteroscedastic Noise Removal

2013 ◽  
Vol 860-863 ◽  
pp. 2936-2939
Author(s):  
Li Yun Su ◽  
Chun Hua Wang
Keyword(s):  
Regression Model ◽  
Polynomial Regression ◽  
Least Squares Method ◽  
Generalized Least Squares ◽  
Noise Removal ◽  
Local Polynomial Regression ◽  
Local Polynomial ◽  
Noise Function ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation

In this paper, we introduce the extension of local polynomial fitting to the linear heteroscedastic regression model and its applications in digital image heteroscedastic noise removal. For better image noise removal with heteroscedastic energy, firstly, the local polynomial regression is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. Due to non-parametric technique of local polynomial estimation, we do not need to know the heteroscedastic noise function. Therefore, we improve the estimation precision, when the heteroscedastic noise function is unknown. Numerical simulations results show that the proposed method can improve the image quality of heteroscedastic noise energy.

ASYMPTOTICALLY EFFICIENT MEDIAN REGRESSION IN THE PRESENCE OF HETEROSKEDASTICITY OF UNKNOWN FORM

2001 ◽  
Vol 17 (4) ◽  
pp. 765-784 ◽  
Author(s):  
Quanshui Zhao
Keyword(s):  
Least Squares Method ◽  
Generalized Least Squares ◽  
Least Absolute Deviation ◽  
Finite Sample ◽  
Median Regression ◽  
Absolute Deviation ◽  
Least Absolute Deviation Regression ◽  
Unknown Form ◽  
The One ◽  
Asymptotically Efficient

We consider a linear model with heteroskedasticity of unknown form. Using Stone's (1977, Annals of Statistics 5, 595–645) k nearest neighbors (k-NN) estimation approach, the optimal weightings for efficient least absolute deviation regression are estimated consistently using residuals from preliminary estimation. The reweighted least absolute deviation or median regression estimator with the estimated weights is shown to be equivalent to the estimator using the true but unknown weights under mild conditions. Asymptotic normality of the estimators is also established. In the finite sample case, the proposed estimators are found to outperform the generalized least squares method of Robinson (1987, Econometrica 55, 875–891) and the one-step estimator of Newey and Powell (1990, Econometric Theory 6, 295–317) based on a Monte Carlo simulation experiment.

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