Abstract
A finite sequence of independent binomial variables is considered for which the null hypothesis of homogeneity is to be tested against the alternative hypotheses of one or two change-points, respectively. The tests are based on the likelihood ratio statistic or on an approximate linearization of the log likelihood ratio statistic. This yields scan type or cusum statistics in a discrete situation. At the same time maximum likelihood or approximate maximum likelihood estimates of the locations of the change-points are derived. For the problem with two change-points — corresponding to the detection of a cluster in time — we distinguish between the cases with a fixed and a variable distance of the two points. Under the null hypothesis exact upper bounds for the upper tails are derived. In the special case of Bernoulli variables these bounds are considerably simplified.
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© 1999 Springer-Verlag Berlin · Heidelberg
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Krauth, J. (1999). Discrete Scan Statistics for Detecting Change-points in Binomial Sequences. In: Gaul, W., Locarek-Junge, H. (eds) Classification in the Information Age. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60187-3_19
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DOI: https://doi.org/10.1007/978-3-642-60187-3_19
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