Bootstrap Inference in Semiparametric Generalized Additive Models

Wolfgang Karl Härdle, Sylvie Huet, Enno Mammen and Stefan Sperlich
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Sylvie Huet: Institut de recherche Agronomique, Postal: Centre de Recherches , de Jouy-en-Josas, F 78352 Jouy-en Josas Cedex, France
Stefan Sperlich: Department de estadística y Econometría, Postal: Universidad Carlos III de Madrid, C/ Madrid 126, E 28903 Getafe, Madrid, Spain

No 01-3, Finance Working Papers from University of Aarhus, Aarhus School of Business, Department of Business Studies

Abstract: Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y , covariates X, T the model is E(Y | X; T) = G { X T β + α + m1(T1) + . . . + md(Td) }. Here, G is a known link, â, á 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 distribution theory for both the non-parametric and the parametric part is given. The main focus is the application of boot-strap methods. It is shown that bootstrap can be used for bias correction, hypothesis testing (e.g. component-wise analysis) and the construction of uniform confidence bands. Various bootstrap tests for model specification and parametrization are given, in particular for testing additivity and link function specification. The practical performance of our methods is illustrated in simulations and in an application to East-West German migration.

Date: Written 2001-03-12
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Journal Article: BOOTSTRAP INFERENCE IN SEMIPARAMETRIC GENERALIZED ADDITIVE MODELS (2004)
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