Scandinavian Working Papers in Business Administration
Finance Working Papers,
University of Aarhus, Aarhus School of Business, Department of Business Studies
No 01-3: Bootstrap Inference in Semiparametric Generalized Additive Models.
Wolfgang Härdle, Sylvie Huet, Enno Mammen () and Stefan Sperlich
Additional contact information
Wolfgang Härdle: Institut für Statistik und Ökonometrie, Postal: Wirtschaftswissenschaftliche Fakultät, Humboldt-Universität zu Berlin, D 10178 Berlin, Germany
Sylvie Huet: Institut de recherche Agronomique, Postal: Centre de Recherches , de Jouy-en-Josas, F 78352 Jouy-en Josas Cedex, France
Enno Mammen: Institut für Angewandte Mathematik, Postal: Ruprecht-Karls-Universität Heidelberg, Im Neuerheimer Feld 294, D 69120 Heidelberg, Germany
Stefan Sperlich: Department de estadística y Econometría, Postal: Universidad Carlos III de Madrid, C/ Madrid 126, E 28903 Getafe, Madrid, Spain
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.
43 pages, March 12, 2001
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