Partially linear estimation using sufficient dimension reduction

Yoshida, Takuma

doi:10.1051/ps/2015018

Yoshida, Takuma ¹

¹ Graduate School of Science and Engineering, Kagoshima University, Kagoshima 890-8580, Japan.

ESAIM: Probability and Statistics, Tome 20 (2016), pp. 1-17.

Résumé

In this paper, we study estimation for partial linear models. We assume radial basis functions for the nonparametric component of these models. To obtain the estimated curve with fitness and smoothness of the nonparametric component, we first apply the sufficient dimension reduction method to the radial basis functions. Then, the coefficients of the transformed radial basis functions are estimated. Finally, the coefficients in the parametric component can be estimated. The above procedure is iterated and hence the proposed method is based on an alternating estimation. The proposed method is highly versatile and is applicable not only to mean regression but also quantile regression and general robust regression. The $\sqrt{n}$ -consistency and asymptotic normality of the estimator are derived. A simulation study is performed and an application to a real dataset is illustrated.

Reçu le : 2015-04-21

MR Zbl

DOI : 10.1051/ps/2015018

Classification : 62F12, 62J02, 62G07
Mots-clés : Partial linear model, robust regression, sliced average variance estimation, sliced inverse regression, sufficient dimension reduction

Affiliations des auteurs :

Yoshida, Takuma ¹

¹ Graduate School of Science and Engineering, Kagoshima University, Kagoshima 890-8580, Japan.

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     publisher = {EDP-Sciences},
     volume = {20},
     year = {2016},
     doi = {10.1051/ps/2015018},
     mrnumber = {3519677},
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     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2015018/}
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Yoshida, Takuma. Partially linear estimation using sufficient dimension reduction. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 1-17. doi : 10.1051/ps/2015018. http://www.numdam.org/articles/10.1051/ps/2015018/

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