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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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1998
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| In: |
Journal of the American Statistical Association
Year: 1998, Volume: 93, Issue: 444, Pages: 1461-1474 |
| ISSN: | 1537-274X |
| DOI: | 10.1080/01621459.1998.10473806 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1080/01621459.1998.10473806 Verlag, Volltext: https://doi.org/10.1080/01621459.1998.10473806 Verlag, kostenfrei, Volltext: http://www.jstor.org/stable/2670060?seq=1#page_scan_tab_contents Verlag, kostenfrei, Volltext: http://www.jstor.org/stable/pdf/2670060.pdf?refreqid=excelsior%3A490697c9c6ebbd6c7d46036889271e9e Verlag, kostenfrei, Volltext: http://www.tandfonline.com/doi/abs/10.1080/01621459.1998.10473806 
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| Author Notes: | Wolfgang Härdle, Enno Mammen, Marlene Müller |
| Summary: | 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. |
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| Item Description: | Published online: 17 February 2012 Gesehen am 13.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1537-274X |
| DOI: | 10.1080/01621459.1998.10473806 |