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Variable selection for semiparametric varying coefficient partially linear models. (English) Zbl 1171.62026
Summary: We present a variable selection procedure by combining basis function approximations with SCAD penalty for semiparametric varying coefficient partially linear models. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of this procedure and the oracle property of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.

62G08Nonparametric regression
62G20Nonparametric asymptotic efficiency
65C05Monte Carlo methods
Full Text: DOI
[1] Fan, J. Q.; Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties, J. amer. Statist. assoc. 96, 1348-1360 (2001) · Zbl 1073.62547 · doi:10.1198/016214501753382273
[2] Fan, J.; Li, R.: New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis, J. amer. Statist. assoc. 99, 710-723 (2004) · Zbl 1117.62329 · doi:10.1198/016214504000001060 · http://masetto.asa.catchword.org/vl=1887686/cl=20/nw=1/rpsv/cw/asa/01621459/v99n467/s20/p710
[3] Fan, J. Q.; Huang, T.: Profile likelihood inference on semiparametric varying-coefficient partially linear models, Bernoulli 11, 1031-1057 (2005) · Zbl 1098.62077 · doi:10.3150/bj/1137421639 · euclid:bj/1137421639
[4] Frank, I. E.; Friedman, J. H.: A statistical view of some chemometrics regression tools, Technometrics 35, 109-148 (1993) · Zbl 0775.62288 · doi:10.2307/1269656
[5] He, X. M.; Zhu, Z. Y.; Fung, W. K.: Estimation in a semiparametric model for longitudinal data with unspecified dependence structure, Biometrika 89, 579-590 (2002) · Zbl 1036.62035 · doi:10.1093/biomet/89.3.579
[6] Hu, X.; Wang, Z.; Zhao, Z.: Empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models, Statist. probab. Lett. 79, 1044-1052 (2009) · Zbl 1158.62030 · doi:10.1016/j.spl.2008.12.011
[7] Huang, Z., Zhang, R., 2009. Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models. Statist. Probab. Lett., in press (doi:10.1016/j.spl.2009.05.008) · Zbl 1169.62028
[8] Leng, C.: A simple approach for varying-coefficient model selection, J. statist. Plann. inference 139, 2138-2146 (2009) · Zbl 1160.62067 · doi:10.1016/j.jspi.2008.10.009
[9] Li, Q.; Huang, C. J.; Li, D.; Fu, T. T.: Semiparametric smooth coefficient models, J. bus. Econom. statist. 20, 412-422 (2002)
[10] Li, R.; Liang, H.: Variable selection in semiparametric regression modeling, Ann. statist. 36, 261-286 (2008) · Zbl 1132.62027 · doi:10.1214/009053607000000604 · euclid:aos/1201877301
[11] Schumaker, L. L.: Spline functions, (1981) · Zbl 0449.41004
[12] Stone, C. J.: Optimal global rates of convergence for nonparametric regression, Ann. statist. 10, 1348-1360 (1982) · Zbl 0511.62048 · doi:10.1214/aos/1176345969
[13] Tibshirani, R.: Regression shrinkage and selection via the LASSO, J. roy. Stat. soc. Ser. B 58, 267-288 (1996) · Zbl 0850.62538
[14] Wang, L.; Chen, G.; Li, H.: Group SCAD regression analysis for microarray time course gene expression data, Bioinformatics 23, 1486-1494 (2007)
[15] Wang, L.; Li, H.; Huang, J. Z.: Variable selection in nonparametric varying-coefficient models for analysis of repeated measurements, J. amer. Statist. assoc. 103, 1556-1569 (2008) · Zbl 1286.62034
[16] Wang, H.J., Zhu, Z., Zhou, J., 2009. Quantile regression in partially linear varying coefficient models. Ann. Statist. (in press) · Zbl 1191.62077
[17] You, J. H.; Zhou, Y.: Empirical likelihood for semiparametric varying-coefficient partially linear regression models, Statist. probab. Lett. 76, 412-422 (2006) · Zbl 1086.62057 · doi:10.1016/j.spl.2005.08.029
[18] Zhang, W.; Lee, S. Y.; Song, X.: Local polynomial Fitting in semivarying coefficient models, J. multivariate anal. 82, 166-188 (2002) · Zbl 0995.62038 · doi:10.1006/jmva.2001.2012
[19] Zou, H.: The adaptive lasso and its oracle properties, J. amer. Statist. assoc. 101, 1418-1429 (2006) · Zbl 1171.62326 · doi:10.1198/016214506000000735