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

Jun Zhang (), Zhenghui Feng () and Peirong Xu ()

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 24, issue 1, 83 pages

Abstract: 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. Copyright Sociedad de Estadística e Investigación Operativa 2015

Keywords: Conditional distribution function; Empirical process; Kernel smoothing; Partial linear models; Single-index; 62G05; 62G08; 62G20 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11749-014-0395-1

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