Buchumschlag

Testing parametric versus semiparametric modeling in generalized linear models

We consider a generalized partially linear model E(Y|X, T) = GX T β + m(T), where G is a known function, β is an unknown parameter vector, and m is an unknown function. We introduce a test statistic that allows one to decide between a parametric and a semiparametric model: (a) m is linear (i.e., m(t...

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Hauptverfasser: Härdle, Wolfgang (VerfasserIn) , Mammen, Enno (VerfasserIn) , Müller, Marlene (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 1998
In: Journal of the American Statistical Association
Year: 1998, Jahrgang: 93, Heft: 444, Pages: 1461-1474
ISSN:1537-274X
DOI:10.1080/01621459.1998.10473806
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Verfasserangaben:Wolfgang Härdle, Enno Mammen, Marlene Müller
Beschreibung
Zusammenfassung:We consider a generalized partially linear model E(Y|X, T) = GX T β + m(T), where G is a known function, β is an unknown parameter vector, and m is an unknown function. We introduce a test statistic that allows one to decide between a parametric and a semiparametric model: (a) m is linear (i.e., m(t) = t T γ for a parameter vector γ), and (b) m is a smooth (nonlinear) function. Under linearity (a), we show that the test statistic is asymptotically normal. Moreover, we prove that the bootstrap works asymptotically. Simulations suggest that (in small samples) the bootstrap outperforms the calculation of critical values from the normal approximation. The practical performance of the test is demonstrated in applications to data on East-West German migration and credit scoring.
Beschreibung:Published online: 17 February 2012
Gesehen am 13.02.2018
Beschreibung:Online Resource
ISSN:1537-274X
DOI:10.1080/01621459.1998.10473806

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