Open Access
February 2012 Projection-type estimation for varying coefficient regression models
Young K. Lee, Enno Mammen, Byeong U. Park
Bernoulli 18(1): 177-205 (February 2012). DOI: 10.3150/10-BEJ331


In this paper we introduce new estimators of the coefficient functions in the varying coefficient regression model. The proposed estimators are obtained by projecting the vector of the full-dimensional kernel-weighted local polynomial estimators of the coefficient functions onto a Hilbert space with a suitable norm. We provide a backfitting algorithm to compute the estimators. We show that the algorithm converges at a geometric rate under weak conditions. We derive the asymptotic distributions of the estimators and show that the estimators have the oracle properties. This is done for the general order of local polynomial fitting and for the estimation of the derivatives of the coefficient functions, as well as the coefficient functions themselves. The estimators turn out to have several theoretical and numerical advantages over the marginal integration estimators studied by Yang, Park, Xue and Härdle [J. Amer. Statist. Assoc. 101 (2006) 1212–1227].


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Young K. Lee. Enno Mammen. Byeong U. Park. "Projection-type estimation for varying coefficient regression models." Bernoulli 18 (1) 177 - 205, February 2012.


Published: February 2012
First available in Project Euclid: 20 January 2012

zbMATH: 1291.62089
MathSciNet: MR2888703
Digital Object Identifier: 10.3150/10-BEJ331

Keywords: kernel smoothing , local polynomial regression , marginal integration , oracle properties , smooth backfitting , varying coefficient models

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability

Vol.18 • No. 1 • February 2012
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