TY  - GEN
Y1  - 1998///
A1  - Härdle, Wolfgang
A1  - Mammen, Enno
A1  - Müller, Marlene
AV  - public
EP  - 35
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/20868/
CY  - Heidelberg
TI  - Testing Parametric versus Semiparametric Modelling in Generalized Linear Models
ID  - heidok20868
N2  - 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.
ER  -