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Projection-Type Estimation for Varying Coefficient Regression Models
Lee, Young K.
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Mammen, Enno
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Park, Byeong U.
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DOI:
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https://doi.org/10.3150/10-BEJ331
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URL:
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http://projecteuclid.org/euclid.bj/1327068622
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Weitere URL:
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http://arxiv.org/pdf/1203.0403.pdf
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Dokumenttyp:
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Zeitschriftenartikel
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Erscheinungsjahr:
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2012
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Titel einer Zeitschrift oder einer Reihe:
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Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability
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Band/Volume:
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18
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Heft/Issue:
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1
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Seitenbereich:
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177-205
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Ort der Veröffentlichung:
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The Hague
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Verlag:
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Bernoulli Soc. for Mathematical Statistics and Probability
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ISSN:
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1350-7265
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Sprache der Veröffentlichung:
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Englisch
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Einrichtung:
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Außerfakultäre Einrichtungen > SFB 884
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Fachgebiet:
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330 Wirtschaft
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Abstract:
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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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