Statistics and Its Interface

Volume 11 (2018)

Number 1

Estimation and variable selection in generalized partially nonlinear models with nonignorable missing responses

Pages: 1 – 18

DOI: https://dx.doi.org/10.4310/SII.2018.v11.n1.a1

Authors

Niansheng Tang (Yunnan Provincial Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming, China)

Lin Tang (Yunnan Provincial Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming, China)

Abstract

Based on the local kernel estimation method and propensity score adjustment method, we develop a penalized likelihood approach to simultaneously select covariates and explanatory variables in the considered parametric respondent model, and estimate parameters and nonparametric functions in generalized partially nonlinear models with nonignorable missing responses. An EM algorithm is proposed to evaluate the penalized likelihood estimations of parameters. The $\mathrm{IC}_Q$ criterion is employed to select the optimal penalty parameter. Under some regularity conditions, we show some asymptotic properties of parameter estimators such as oracle property. It can be shown that the proposed local linear kernel estimator of the nonparametric component is an estimator of a least favorable curve. The consistency of the $\mathrm{IC}_Q$-based selection procedure is obtained. Simulation studies are conducted, and a real data set is used to illustrate the proposed methodologies.

Keywords

generalized partially nonlinear models, local kernel estimation, nonignorable missing responses, propensity score, variable selection

Received 9 June 2016

Published 23 August 2017