Estimating the conditional single-index error distribution with a partial linear mean regression
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Jun Zhang [1] ; Zhenghui Feng [2] ; Peirong Xu [3]
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[1] Shenzhen University
Shenzhen University
China
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[2] Xiamen University
Xiamen University
China
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[3] Southeast University
Southeast University
China
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 24, Nº. 1, 2015, págs. 61-83
- Idioma: inglés
- DOI: 10.1007/s11749-014-0395-1
- Texto completo no disponible (Saber más ...)
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Resumen
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
