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BOOTSTRAP INFERENCE IN SEMIPARAMETRIC GENERALIZED ADDITIVE MODELS

Published online by Cambridge University Press:  10 February 2004

Wolfgang Härdle ,
Sylvie Huet ,
Enno Mammen  and
Stefan Sperlich
Wolfgang Härdle
Affiliation:
Humboldt-Universität zu Berlin
Sylvie Huet
Affiliation:
Institut de Recherche Agronomique
Enno Mammen
Affiliation:
Universität Mannheim
Stefan Sperlich
Affiliation:
Universidad Carlos III de Madrid
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Abstract

Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y, covariates X,T, the considered model is E(Y |X;T) = G{XTβ + α + m1(T1) + ··· + md(Td)}. Here, G is a known link, α and β are unknown parameters, and m1,…,md are unknown (smooth) functions of possibly higher dimensional covariates T1,…,Td. Estimates of m1,…,md, α, and β are presented, and asymptotic distributions are given for both the nonparametric and the parametric part. The main focus of the paper is application of bootstrap methods. It is shown how bootstrap can be used for bias correction, hypothesis testing (e.g., component-wise analysis), and the construction of uniform confidence bands. Further, bootstrap tests for model specification and parametrization are given, in particular for testing additivity and link function specification. The practical performance of the methods is illustrated in a simulation study.This research was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 373 “Quantifikation und Simulation ökonomischer Prozesse,” Humboldt-Universität zu Berlin, DFG project MA 1026/6-2, the Spanish “Dirección General de Enseñanza Superior,” no. BEC2001-1270, and the grant “Nonparametric methods in finance and insurance” from the Danish Social Science Research Council. We thank Marlene Müller, Oliver Linton, and two anonymous referees for helpful discussion.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 2 , April 2004 , pp. 265 - 300
Copyright
© 2004 Cambridge University Press

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