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Testing Parametric versus Semiparametric Modelling in Generalized Linear Models

Härdle, Wolfgang ; Mammen, Enno ; Müller, Marlene

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Abstract

We consider a genralized partially linear model E(Y | X,T) = G{ X^T beta + m(T) } where G is a known function, beta is an unknown parameter vector, and m is an unknown function. The paper introduces a test statistic which allows to decide between a parametric and a semiparametric model:(i) m is linear, i.e. m(t) = t^T gamma for a parameter vector gamma,(ii) m is a smooth (nonlinear) function. Under linearity (i) it is shown that the test statistic is asymptotically normal. Moreover, it is proved that the bootstrap works asymptotically. Simulations suggest that (in small samples) bootstrap outperforms the calculation of critical values from the normal approximation. The practical performance of the test is shown in applications to data on East-West German migration and credit scoring.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 07 Jun 2016 07:55
Date: 1998
Number of Pages: 35
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
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