Projection-type estimation for varying coefficient regression models
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...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
20 January 2012
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| In: |
Bernoulli
Year: 2012, Volume: 18, Issue: 1, Pages: 177-205 |
| ISSN: | 1573-9759 |
| DOI: | 10.3150/10-BEJ331 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.3150/10-BEJ331 Verlag, Volltext: https://projecteuclid.org/euclid.bj/1327068622 Verlag, Volltext: https://projecteuclid.org/download/pdfview_1/euclid.bj/1327068622 
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| Author Notes: | Young K. Lee, Enno Mammen, Byeong U. Park |
| Summary: | 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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| Item Description: | Gesehen am 31.01.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1573-9759 |
| DOI: | 10.3150/10-BEJ331 |