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| Weighted Profile Least Squares Estimation for a Panel Data Varying-Coefficient Partially Linear Model |
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Citation： |
Bin ZHOU,Jinhong YOU,Qinfeng XU,Gemai CHEN.Weighted Profile Least Squares Estimation for a Panel Data Varying-Coefficient Partially Linear Model[J].Chinese Annals of Mathematics B,2010,31(2):247~272 |
| Page view： 1738
Net amount： 2424 |
Authors： |
Bin ZHOU; Jinhong YOU; Qinfeng XU; Gemai CHEN; |
Foundation： |
the Leading Academic Discipline Program, 211 Project for Shanghai University
of Finance and Economics (the 3rd phase) (No. B803) and the Shanghai Leading Academic Discipline
Project (No. B210). |
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| Abstract： |
This paper is concerned with inference of panel data varying-coefficient par-
tially linear models with a one-way error structure. The model is a natural extension of the
well-known panel data linear model (due to Baltagi 1995) to the setting of semiparamet-
ric regressions. The authors propose a weighted profile least squares estimator (WPLSE)
and a weighted local polynomial estimator (WLPE) for the parametric and nonparametric
components, respectively. It is shown that the WPLSE is asymptotically more efficient
than the usual profile least squares estimator (PLSE), and that the WLPE is also asymp-
totically more efficient than the usual local polynomial estimator (LPE). The latter is an
interesting result. According to Ruckstuhl, Welsh and Carroll (2000) and Lin and Car-
roll (2000), ignoring the correlation structure entirely and “pretending” that the data are
really independent will result in more efficient estimators when estimating nonparametric
regression with longitudinal or panel data. The result in this paper shows that this is not
true when the design points of the nonparametric component have a closeness property
within groups. The asymptotic properties of the proposed weighted estimators are derived.
In addition, a block bootstrap test is proposed for the goodness of fit of models, which can
accommodate the correlations within groups. Some simulation studies are conducted to
illustrate the finite sample performances of the proposed procedures. |
Keywords： |
Semiparametric, Panel data, Local polynomial, Weighted estimation,
Block bootstrap |
Classification： |
62H12, 62A10 |
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