# Empirical likelihood for heteroscedastic partially linear single-index models with growing dimensional data

Jianglin Fang (), Wanrong Liu and Xuewen Lu
Jianglin Fang: Hunan Institute of Engineering
Wanrong Liu: Hunan Normal University
Xuewen Lu: University of Calgary

Metrika: International Journal for Theoretical and Applied Statistics, 2018, vol. 81, issue 3, 255-281

Abstract: Abstract In this paper, we propose a new approach to the empirical likelihood inference for the parameters in heteroscedastic partially linear single-index models. In the growing dimensional setting, it is proved that estimators based on semiparametric efficient score have the asymptotic consistency, and the limit distribution of the empirical log-likelihood ratio statistic for parameters $$(\beta ^{\top },\theta ^{\top })^{\top }$$ ( β ⊤ , θ ⊤ ) ⊤ is a normal distribution. Furthermore, we show that the empirical log-likelihood ratio based on the subvector of $$\beta$$ β is an asymptotic chi-square random variable, which can be used to construct the confidence interval or region for the subvector of $$\beta$$ β . The proposed method can naturally be applied to deal with pure single-index models and partially linear models with high-dimensional data. The performance of the proposed method is illustrated via a real data application and numerical simulations.

Keywords: Empirical likelihood; High-dimensional data; Heteroscedasticity; Partially linear single-index model; Semiparametric efficiency (search for similar items in EconPapers)
Date: 2018
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