Abstract
In this chapter, Poisson approximation for multiple scan statistics in the continuous case is investigated. The setting is mainly two dimensional, but higher dimensions are also discussed. The scanning set can be any convex set, and in order to motivate the choice of parameters in the approximations, some geometrical arguments are given. The errors involved in the approximations are studied both by simulations and by giving bounds on the total variation distances by means of the Stein—Chen method. Furthermore, Poisson process approximations of some point processes, which occur in this context, are considered.
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Månsson, M. (1999). On Poisson Approximation for Continuous Multiple Scan Statistics in Two Dimensions. In: Glaz, J., Balakrishnan, N. (eds) Scan Statistics and Applications. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1578-3_10
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DOI: https://doi.org/10.1007/978-1-4612-1578-3_10
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7201-4
Online ISBN: 978-1-4612-1578-3
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