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Characterization of distributions from maximal invariant statistics (1983)

Small, Christopher G.

Springer

Probability theory and related fields 63 (1983), S. 517-527

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ISSN: 1432-2064

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary G.W. Brown, Yu.V. Prokhorov, L. Bondesson and others have developed characterization results for maximal invariant statistics. Such results show that it is possible to construct tests to distinguish between types of distributions. In this paper, these results are proved for a large number of cases that arise in particular in spatial statistics and directional statistics. The class of n-collected distributions, n≧3, is introduced. It is proved that if a distribution is n-collected then a sample of size n has sufficient information to distinguish the type of the distribution. In other words, the distribution of the maximal invariant characterizes type.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00533725

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