Chinese Annals of Mathematics, Series B

, Volume 31, Issue 2, pp 247–272 | Cite as

Weighted profile least squares estimation for a panel data varying-coefficient partially linear model

  • Bin Zhou
  • Jinhong You
  • Qinfeng XuEmail author
  • Gemai Chen


This paper is concerned with inference of panel data varying-coefficient partially 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 semiparametric 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 asymptotically 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 Carroll (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.


Semiparametric Panel data Local polynomial Weighted estimation Block bootstrap 

2000 MR Subject Classification

62H12 62A10 


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Copyright information

© Editorial Office of CAM (Fudan University) and Springer Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of Finance and StatisticsEast China Normal UniversityShanghaiChina
  2. 2.Department of StatisticsShanghai University of Finance and EconomicsShanghaiChina
  3. 3.School of ManagementFudan UniversityShanghaiChina
  4. 4.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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