Empirical Likelihood Inferences for Semiparametric Varying-Coefficient Partially Linear Models with Longitudinal Data

Abstract

Abstract In this article, empirical likelihood inferences for semiparametric varying-coefficient partially linear models with longitudinal data are investigated. We propose a groupwise empirical likelihood procedure to handle the inter-series dependence of the longitudinal data. By using residual-adjustment, an empirical likelihood ratio function for the nonparametric component is constructed, and a nonparametric version Wilks' phenomenons is proved. Compared with methods based on normal approximations, the empirical likelihood does not require consistent estimators for the asymptotic variance and bias. A simulation study is undertaken to assess the finite sample performance of the proposed confidence regions. Keywords: Empirical likelihoodLongitudinal dataSemiparametric varying-coefficient partially linear modelMathematics Subject Classification: Primary 62G05Secondary 62G20 Acknowledgments This research was supported by the National Natural Science Foundation of China (10871013), the Natural Science Foundation of Beijing (1102008), the Natural Science Foundation of Guangxi (2010GXNXSFB013051), the Graduate Student Foundation of Hechi University (2008QS-N014), and the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (IHLB).