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

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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.

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Acknowledgments

The authors thank the editor, the associate editor, and two referees for their constructive suggestions that helped us to improve the early manuscript. Zhang’s research was supported by the National Natural Science Foundation of China (NSFC), Tianyuan fund for Mathematics, No. 11326179, and NSFC grant No. 11401391. Feng’s research was supported by the NSFC grant No. 11301434. Xu’s research was supported by the NSFC grant No. 11101157, and the Natural Science Foundation of Jiangsu Province, China, grant No. BK20140617. The paper is partially supported by the NSFC grant No. 11101063, No. 11201306, and No. 11201499.

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Authors and Affiliations

  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

    Jun Zhang

  2. School of Economics and the Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, China

    Zhenghui Feng

  3. Department of Mathematics, Southeast University, Nanjing, China

    Peirong Xu

Authors
  1. Jun Zhang
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  2. Zhenghui Feng
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  3. Peirong Xu
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Correspondence to Zhenghui Feng.

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Zhang, J., Feng, Z. & Xu, P. Estimating the conditional single-index error distribution with a partial linear mean regression. TEST 24, 61–83 (2015). https://doi.org/10.1007/s11749-014-0395-1

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  • DOI: https://doi.org/10.1007/s11749-014-0395-1

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