Estimating the Conditional Single-Index Error Distribution with A Partial Linear Mean Regression-Wang Yanan Institute for Studies in Economics (WISE), Xiamen University

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作者	Jun Zhang, Zhenghui Feng, Peirong Xu
正文	In this paper,we present amethod for estimating the conditional distribution function of the model error. Given the covariates, the conditional mean function is modeled as a partial linear model, and the conditional distribution function of model error is modeled as a single-index model. To estimate the single-index parameter, we propose a semi-parametric global weighted least-squares estimator coupled with an indicator function of the residuals. We derive a residual-based kernel estimator to estimate the unknown conditional distribution function. Asymptotic distributions of the proposed estimators are derived, and the residual-based kernel process constructed by the estimator of the conditional distribution function is shown to converge to a Gaussian process. Simulation studies are conducted and a real dataset is analyzed to demonstrate the performance of the proposed estimators.
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关键词：	Conditional distribution function · Empirical process · Kernel smoothing · Partial linear models · Single-index