Bernoulli

  • Bernoulli
  • Volume 18, Number 1 (2012), 177-205.

Projection-type estimation for varying coefficient regression models

Young K. Lee, Enno Mammen, and Byeong U. Park

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Abstract

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].

Article information

Source
Bernoulli, Volume 18, Number 1 (2012), 177-205.

Dates
First available in Project Euclid: 20 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.bj/1327068622

Digital Object Identifier
doi:10.3150/10-BEJ331

Mathematical Reviews number (MathSciNet)
MR2888703

Zentralblatt MATH identifier
1291.62089

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

Citation

Lee, Young K.; Mammen, Enno; Park, Byeong U. Projection-type estimation for varying coefficient regression models. Bernoulli 18 (2012), no. 1, 177--205. doi:10.3150/10-BEJ331. https://projecteuclid.org/euclid.bj/1327068622


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