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Error variance estimation in semi-functional partially linear regression models

Author

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  • Germán Aneiros
  • Nengxiang Ling
  • Philippe Vieu

Abstract

This paper focuses on partially linear regression models with several real and functional covariates. The aim is to construct an estimate of the variance of the error. In our model, a real-valued response variable is explained by the sum of an unknown linear combination of the components of a multivariate random variable and an unknown transformation of a functional random variable, and the second sample moment based on residuals from a semiparametric fit is proposed for estimating the error variance. Then, the asymptotic normality and the law of the iterated logarithm of such estimator are obtained. Finally, a simulation study illustrates the finite sample behaviour of the estimator, while an application to real data shows the usefulness of the proposed methodology, more specifically for confidence region construction.

Suggested Citation

  • Germán Aneiros & Nengxiang Ling & Philippe Vieu, 2015. "Error variance estimation in semi-functional partially linear regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 316-330, September.
  • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:316-330
    DOI: 10.1080/10485252.2015.1042376
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    File URL: http://hdl.handle.net/10.1080/10485252.2015.1042376
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    References listed on IDEAS

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    1. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    2. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    3. repec:taf:gnstxx:v:23:y:2011:i:1:p:115-128 is not listed on IDEAS
    4. Tiejun Tong & Yuedong Wang, 2005. "Estimating residual variance in nonparametric regression using least squares," Biometrika, Biometrika Trust, vol. 92(4), pages 821-830, December.
    5. Isabel Casas & Irene Gijbels, 2012. "Unstable volatility: the break-preserving local linear estimator," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 883-904, December.
    6. Gao, Jiti, 1995. "The laws of the iterated logarithm of some estimates in partly linear models," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 153-162, November.
    7. Maity, Arnab & Huang, Jianhua Z., 2012. "Partially linear varying coefficient models stratified by a functional covariate," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1807-1814.
    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.
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    Cited by:

    1. Boente, Graciela & Vahnovan, Alejandra, 2017. "Robust estimators in semi-functional partial linear regression models," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 59-84.
    2. repec:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-017-0786-3 is not listed on IDEAS

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