Issue |
ESAIM: PS
Volume 20, 2016
|
|
---|---|---|
Page(s) | 1 - 17 | |
DOI | https://doi.org/10.1051/ps/2015018 | |
Published online | 03 June 2016 |
Partially linear estimation using sufficient dimension reduction
Graduate School of Science and Engineering, Kagoshima University, Kagoshima
890-8580, Japan.
yoshida@sci.kagoshima-u.ac.jp
Received:
21
April
2015
Revised:
27
November
2015
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 -consistency and asymptotic normality of the estimator
are derived. A simulation study is performed and an application to a real dataset is
illustrated.
Mathematics Subject Classification: 62F12 / 62J02 / 62G07
Key words: Partial linear model / robust regression / sliced average variance estimation / sliced inverse regression / sufficient dimension reduction
© EDP Sciences, SMAI 2016
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