An interpretation and some generalizations of the Anderson–Darling statistics in terms of squared Bessel bridges

Some generalizations of the Anderson–Darling statistics are presented, as well as their representations as functions of Bessel processes. Combining these results with some computations of Donati–Martin–Yor (Ann. Probab. 25(3) (1997) 1011–1058), standard results are recovered.

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Veröffentlicht in:	Statistics & probability letters 2005-04, Vol.72 (2), p.171-177
1. Verfasser:	Mansuy, Roger
Format:	Artikel
Sprache:	eng
Schlagworte:	Anderson-Darling statistics Quadratic functionals Bessel processes Anderson–Darling statistics Bessel processes Distribution theory Exact sciences and technology Markov processes Mathematics Probability Probability and statistics Probability theory and stochastic processes Quadratic functionals Sciences and techniques of general use Statistics
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Beschreibung
Zusammenfassung:	Some generalizations of the Anderson–Darling statistics are presented, as well as their representations as functions of Bessel processes. Combining these results with some computations of Donati–Martin–Yor (Ann. Probab. 25(3) (1997) 1011–1058), standard results are recovered.
ISSN:	0167-7152 1879-2103
DOI:	10.1016/j.spl.2005.01.001