On a Goodness-of-Fit Test for Multiplicative Poisson Models

Abstract

A model for random $n \times k$ matrices $X$ is considered. The elements $X_{ij}$ are assumed to be independent and Poisson-distributed random variables with means $\alpha_i\exp(\gamma t'_{ij})$, where $t_{ij}$ are known $m$-dimensional vectors and $(\alpha, \gamma)$ is an unknown parameter. A goodness-of-fit test is proposed and an approximation is derived when the number $n$ of rows is large.