Testing for the bivariate Poisson distribution. (English) Zbl 1304.62043
Summary: This paper studies goodness-of-fit tests for the bivariate Poisson distribution. Specifically, we propose and study several Cramér-von Mises type tests based on the empirical probability generating function. They are consistent against fixed alternatives for adequate choices of the weight function involved in their definition. They are also able to detect local alternatives converging to the null at a certain rate. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approximation and compares their powers for finite sample sizes. Extensions for testing goodness-of-fit for the multivariate Poisson distribution are also discussed.
MSC:
| 62F03 | Parametric hypothesis testing |
| 62F40 | Bootstrap, jackknife and other resampling methods |
| 62F05 | Asymptotic properties of parametric tests |
| 62F10 | Point estimation |
Keywords:
bivariate Poisson distribution; goodness-of-fit; empirical probability generating function; consistency against fixed alternatives; local alternatives; bootstrap distribution estimatorSoftware:
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