BOOTSTRAP INFERENCE IN SEMIPARAMETRIC GENERALIZED ADDITIVE MODELS

Wolfgang H rdle, Sylvie Huet, Enno Mammen and Stefan Sperlich

Econometric Theory, 2004, vol. 20, issue 02, pages 265-300

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{XT + + m1(T1) + + md(Td)}. Here, G is a known link, and are unknown parameters, and m1, , md are unknown (smooth) functions of possibly higher dimensional covariates T1, ,Td. Estimates of m1, , md, , and 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.

Date: 2004
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