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Statistical inference using a weighted difference-based series approach for partially linear regression models

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  • Ai, Chunrong
  • You, Jinhong
  • Zhou, Yong

Abstract

Partially linear regression models with fixed effects are useful tools for making econometric analyses and normalizing microarray data. Baltagi and Li (2002) [7] proposed a computation friendly difference-based series estimation (DSE) for them. We show that the DSE is not asymptotically efficient in most cases and further propose a weighted difference-based series estimation (WDSE). The weights in it do not involve any unknown parameters. The asymptotic properties of the resulting estimators are established for both balanced and unbalanced cases, and it is shown that they achieve a semiparametric efficient boundary. Additionally, we propose a variable selection procedure for identifying significant covariates in the parametric part of the semiparametric fixed-effects regression model. The method is based on a combination of the nonconcave penalization (Fan and Li, 2001 [13]) and weighted difference-based series estimation techniques. The resulting estimators have the oracle property; that is, they can correctly identify the true model as if the true model (the subset of variables with nonvanishing coefficients) were known in advance. Simulation studies are conducted and an application is given to demonstrate the finite sample performance of the proposed procedures.

Suggested Citation

  • Ai, Chunrong & You, Jinhong & Zhou, Yong, 2011. "Statistical inference using a weighted difference-based series approach for partially linear regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 601-618, March.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:601-618
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    References listed on IDEAS

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    1. Badi H. Baltagi & Dong Li, 2002. "Series Estimation of Partially Linear Panel Data Models with Fixed Effects," Annals of Economics and Finance, Society for AEF, vol. 3(1), pages 103-116, May.
    2. Lichtenberg, Frank R, 1988. "Estimation of the Internal Adjustment Costs Model Using Longitudinal Establishment Data," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 421-430, August.
    3. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying‐coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80, February.
    4. Ash A. Alizadeh & Michael B. Eisen & R. Eric Davis & Chi Ma & Izidore S. Lossos & Andreas Rosenwald & Jennifer C. Boldrick & Hajeer Sabet & Truc Tran & Xin Yu & John I. Powell & Liming Yang & Gerald E, 2000. "Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling," Nature, Nature, vol. 403(6769), pages 503-511, February.
    5. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
    6. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(3), pages 560-586, June.
    7. Duffy, John & Papageorgiou, Chris, 2000. "A Cross-Country Empirical Investigation of the Aggregate Production Function Specification," Journal of Economic Growth, Springer, vol. 5(1), pages 87-120, March.
    8. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    9. Delecroix, Michel & Härdle, Wolfgang & Hristache, Marian, 2003. "Efficient estimation in conditional single-index regression," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 213-226, August.
    10. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    11. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
    12. Fan, Jianqing & Peng, Heng & Huang, Tao, 2005. "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 781-796, September.
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    Cited by:

    1. Liping Zhu & Jinhong You & Qunfang Xu, 2014. "Statistical Inference for Single-index Panel Data Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 830-843, September.
    2. Hu, Jianhua & You, Jinhong & Zhou, Xian, 2017. "Improved estimation of fixed effects panel data partially linear models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 96-111.

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