Abstract

Semiparametric estimation in single index Poisson regression: a practical approach

D. CLIMOV, M. DELECROIX and L. SIMAR

In a single index Poisson regression model with unknown link function, the index parameter can be root-n consistently estimated by the method of a pseudo maximum likelihood. In this paper, we study, by simulation arguments, the practical validity of the aymptotic behaviour of the pseudo maximum likelihood index estimator and os 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.

  Last update: January, 10, 2003  - Contact : S. Malali