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

Abstract

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.Anderson-Darling statistics Quadratic functionals Bessel processes