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Tail probabilities for the null distribution of scanning statistics. (English) Zbl 0976.62048

Summary: This paper is concerned with statistics that scan a multidimensional spatial region to detect a signal against a noisy background. The background is modelled as independent observations from an exponential family of distributions with a known ‘null’ value of the natural parameter, while the signal is given by independent observations from the same exponential family, but with a different value of the parameter on a particular subregion of the spatial domain.
The main result is an extension to multidimensional time of the method of M. Pollak and B. Yakir [Ann. Appl. Probab. 8, No. 3, 749-774 (1998; Zbl 0937.60082)], which relies on a change of measure motivated by change-point analysis, to evaluate approximately the null distribution of the likelihood ratio statistic. Both large-deviation and Poisson approximations are obtained.

MSC:

62H10 Multivariate distribution of statistics
62E20 Asymptotic distribution theory in statistics
62E15 Exact distribution theory in statistics

Citations:

Zbl 0937.60082
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