Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics
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 notewort...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/696927 |
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| _version_ | 1849685487813394432 |
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| author | Liyun Su Yanyong Zhao Tianshun Yan |
| author_facet | Liyun Su Yanyong Zhao Tianshun Yan |
| author_sort | Liyun Su |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bf5778cae4f94c00a9ccfe3d572643b3 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-bf5778cae4f94c00a9ccfe3d572643b32025-08-20T03:23:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/696927696927Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in EconomicsLiyun Su0Yanyong Zhao1Tianshun Yan2School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaSchool of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaSchool of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaWe 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.http://dx.doi.org/10.1155/2012/696927 |
| spellingShingle | Liyun Su Yanyong Zhao Tianshun Yan Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics Discrete Dynamics in Nature and Society |
| title | Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics |
| title_full | Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics |
| title_fullStr | Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics |
| title_full_unstemmed | Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics |
| title_short | Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics |
| title_sort | two stage method based on local polynomial fitting for a linear heteroscedastic regression model and its application in economics |
| url | http://dx.doi.org/10.1155/2012/696927 |
| work_keys_str_mv | AT liyunsu twostagemethodbasedonlocalpolynomialfittingforalinearheteroscedasticregressionmodelanditsapplicationineconomics AT yanyongzhao twostagemethodbasedonlocalpolynomialfittingforalinearheteroscedasticregressionmodelanditsapplicationineconomics AT tianshunyan twostagemethodbasedonlocalpolynomialfittingforalinearheteroscedasticregressionmodelanditsapplicationineconomics |