Generalized varying coefficient partially linear measurement errors models

We study generalized varying coefficient partially linearmodels when some linear covariates are error prone, but their ancillary variables are available. We first calibrate the error-prone covariates, then develop a quasi-likelihood-based estimation procedure. To select significant variables in the parametric part, we develop a penalized quasi-likelihood variable selection procedure, and the resulting penalized estimators are shown to be asymptotically normal and have the oracle property. Moreover, to select significant variables in the nonparametric component, we investigate asymptotic behavior of the semiparametric generalized likelihood ratio test. The limiting null distribution is shown to follow aChi-square distribution, and a newWilks phenomenon Electronic supplementary material The online version of this article (doi:10.1007/s10463-015-0532-y) contains supplementary material, which is available to authorized users. B Jun Zhang [email protected] Zhenghui Feng [email protected] Peirong Xu [email protected] Hua Liang [email protected] 1 Shen Zhen-Hong Kong Joint Research Centre for Applied Statistical Sciences, School of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University, Shenzhen 518060, China 2 School of Economics, and the Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen 361005, China 3 Department of Mathematics, Southeast University, Nanjing 211189, China 4 Department of Statistics, George Washington University, Washington, DC 20052, USA