Estimating the Conditional Single-Index Error Distribution with A Partial Linear Mean Regression
Jun Zhang, Zhenghui Feng, Peirong Xu
Test Volume 24, Issue 1 , pp 61-83
#002279 20160221 ()
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.
Keywords: Conditional distribution function · Empirical process · Kernel smoothing · Partial linear models · Single-index

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