Semiparametric estimation in single index poisson regression: A practical approach - Daniela Climov; Michel Delecroix; Léopold Simar (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 2001)
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 maximumum likelihood. In this paper, we study, by simulation arguments, the practical validity of the asymptotic behavior 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 situtations. The procedure is illustrated through a real data example.
urn:nbn:de:kobv:11-10050028
Keywords: 330; single index models; Poisson regression; kernel estimation; bandwidth selection; bootstrap