WILKS' THEOREM FOR SEMIPARAMETRIC REGRESSIONS WITH WEAKLY DEPENDENT DATA

• 成果类型: Article
• 署名作者: de Chaumaray, Marie du Roy; Marbac, Matthieu; Patilea, Valentin
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Rennes; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2081
• 发表日期: 2021
• 页码: 3228-3254
• 关键词: empirical likelihood inference; partial linear-models; single-index models; mixing properties; geometric ergodicity; time-series; ARCH; CONVERGENCE

摘要

The empirical likelihood inference is extended to a class of semiparametric models for stationary, weakly dependent series. A partially linear single-index regression is used for the conditional mean of the series given its past, and the present and past values of a vector of covariates. A parametric model for the conditional variance of the series is added to capture further nonlinear effects. We propose suitable moment equations which characterize the mean and variance model. We derive an empirical log-likelihood ratio which includes nonparametric estimators of several functions, and we show that this ratio behaves asymptotically as if the functions were given.