Estimating the conditional single-index error distribution with a partial linear mean regression

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• 作者：Jun Zhang (1)
  Zhenghui Feng (2)
  Peirong Xu (3)
  
  1. Shen Zhen-Hong Kong Joint Research Center for Applied Statistical Sciences ; College of Mathematics and Computational Science ; Institute of Statistical Sciences at Shenzhen University ; Shenzhen University ; Shenzhen ; China
  2. School of Economics and the Wang Yanan Institute for Studies in Economics ; Xiamen University ; Xiamen ; China
  3. Department of Mathematics ; Southeast University ; Nanjing ; China
  
• 关键词：Conditional distribution function ; Empirical process ; Kernel smoothing ; Partial linear models ; Single ; index ; 62G05 ; 62G08 ; 62G20
• 刊名：TEST
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：24
• 期：1
• 页码：61-83
• 全文大小：449 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistical Theory and Methods
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1863-8260

文摘

In this paper, we present a method 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.