## The Annals of Statistics

- Ann. Statist.
- Volume 9, Number 4 (1981), 697-704.

### 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.

#### Article information

**Source**

Ann. Statist., Volume 9, Number 4 (1981), 697-704.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345512

**Digital Object Identifier**

doi:10.1214/aos/1176345512

**Mathematical Reviews number (MathSciNet)**

MR619276

**Zentralblatt MATH identifier**

0471.62049

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62H15: Hypothesis testing

Secondary: 62P99: None of the above, but in this section

**Keywords**

Multiplicative Poisson model exact test asymptotic distribution conditional limit theorem

#### Citation

Svensson, Ake. On a Goodness-of-Fit Test for Multiplicative Poisson Models. Ann. Statist. 9 (1981), no. 4, 697--704. doi:10.1214/aos/1176345512. https://projecteuclid.org/euclid.aos/1176345512