Semiparametric estimation in single index Poisson regression: a practical approach

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.