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Semiparametric estimation in single index Poisson regression: a practical approach

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Climov, Daniela Delecroix, Michel Simar, Léopold [UCL]

In a single index Poisson regression model with unknown link function, the index parameter can be root-n consistently estimated by the method of pseudo maximum likelihood. In this paper, we study, by simulation arguments, the practical validity of the asymptotic behaviour of the pseudo maximum likelihood index estimator and of some associated cross-validation bandwidths. A robust practical rule for implementing the pseudo maximum likelihood estimation method is suggested, which uses the bootstrap for estimating the variance of the index estimator and a variant of bagging for numerically stabilizing its variance. Our method gives reasonable results even for moderate sized samples; thus, it can be used for doing statistical inference in practical situations. The procedure is illustrated through a real data example.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2002
Language Anglais
Journal information "Journal of Applied Statistics" - Vol. 29, no. 7, p. 1047-1070 (2002)
Peer reviewed yes
Publisher Carfax Publishing (Basingstoke)
issn 0266-4763
e-issn 1360-0532
Publication status Publié
Affiliation UCL - EUEN/STAT - Institut de statistique
Links
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Bibliographic reference Climov, Daniela ; Delecroix, Michel ; Simar, Léopold. Semiparametric estimation in single index Poisson regression: a practical approach. In: Journal of Applied Statistics, Vol. 29, no. 7, p. 1047-1070 (2002)
Permanent URL http://hdl.handle.net/2078.1/41718