Siegmund, David; Yakir, Benjamin Tail probabilities for the null distribution of scanning statistics. (English) Zbl 0976.62048 Bernoulli 6, No. 2, 191-213 (2000). 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. Cited in 35 Documents MSC: 62H10 Multivariate distribution of statistics 62E20 Asymptotic distribution theory in statistics 62E15 Exact distribution theory in statistics Keywords:scan statistic; Markov inequality; multidimensional exponential families; change-point analysis; likelihood ratio Citations:Zbl 0937.60082 PDFBibTeX XMLCite \textit{D. Siegmund} and \textit{B. Yakir}, Bernoulli 6, No. 2, 191--213 (2000; Zbl 0976.62048) Full Text: DOI Link