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

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  • Jun Zhang
  • Zhenghui Feng
  • Peirong Xu

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

Suggested Citation

  • Jun Zhang & Zhenghui Feng & Peirong Xu, 2015. "Estimating the conditional single-index error distribution with a partial linear mean regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 61-83, March.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:1:p:61-83
    DOI: 10.1007/s11749-014-0395-1
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    References listed on IDEAS

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    1. Neumeyer, N. & Van Keilegom, I., 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," LIDAM Reprints ISBA 2010006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    3. Neumeyer, Natalie, 2009. "Testing independence in nonparametric regression," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1551-1566, August.
    4. Einmahl, J.H.J. & van Keilegom, I., 2006. "Tests for Independence in Nonparametric Regression," Other publications TiSEM 0c6f2c43-aa7d-45c1-9d43-7, Tilburg University, School of Economics and Management.
    5. Liang, Hua & Li, Runze, 2009. "Variable Selection for Partially Linear Models With Measurement Errors," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 234-248.
    6. Zhu, Lixing & Lin, Lu & Cui, Xia & Li, Gaorong, 2010. "Bias-corrected empirical likelihood in a multi-link semiparametric model," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 850-868, April.
    7. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    8. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    9. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
    10. Sebastian Kiwitt & Natalie Neumeyer, 2013. "A note on testing independence by a copula-based order selection approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 62-82, March.
    11. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    12. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    13. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    14. Kong, Efang & Xia, Yingcun, 2012. "A Single-Index Quantile Regression Model And Its Estimation," Econometric Theory, Cambridge University Press, vol. 28(4), pages 730-768, August.
    15. Golubev, Georgi & Härdle, Wolfgang, 2000. "On adaptive estimation in partial linear models," SFB 373 Discussion Papers 2000,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    16. Sebastian Kiwitt & Natalie Neumeyer, 2012. "Estimating the Conditional Error Distribution in Non-parametric Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 259-281, June.
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    Cited by:

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    2. Jun Zhang, 2021. "Model checking for multiplicative linear regression models with mixed estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 364-403, August.
    3. Zhang, Jun & Lin, Bingqing & Zhou, Yan, 2021. "Kernel density estimation for partial linear multivariate responses models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).

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