Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors |
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Authors: | Jinhong You Yong Zhou |
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Institution: | a Department of Statistics, Shanghai University of Finance and Economics, Shanghai, China b Department of Actuarial Studies, Macquarie University, Sydney, New South Wales, Australia c Institute of Applied Mathematics, Chinese Academy of Science, Beijing, China |
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Abstract: | We consider a panel data semiparametric partially linear regression model with an unknown parameter vector for the linear parametric component, an unknown nonparametric function for the nonlinear component, and a one-way error component structure which allows unequal error variances (referred to as heteroscedasticity). We develop procedures to detect heteroscedasticity and one-way error component structure, and propose a weighted semiparametric least squares estimator (WSLSE) of the parametric component in the presence of heteroscedasticity and/or one-way error component structure. This WSLSE is asymptotically more efficient than the usual semiparametric least squares estimator considered in the literature. The asymptotic properties of the WSLSE are derived. The nonparametric component of the model is estimated by the local polynomial method. Some simulations are conducted to demonstrate the finite sample performances of the proposed testing and estimation procedures. An example of application on a set of panel data of medical expenditures in Australia is also illustrated. |
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Keywords: | primary 62H12 62G08 secondary 62G20 62F12 |
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