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

Statistics and Probability Letters

Volumn 72, Issue 2, 2005, Pages 171-177

  Mansuy, Roger ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Anderson Darling statistics; Bessel processes; Quadratic functionals

Indexed keywords

EID: 15844426888     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2005.01.001     Document Type: Article

References (12)

1. T.W. Anderson D.A. Darling A test of goodness of fit J. Amer. Statist. Assoc. 49 1954 765-769
2. Ph. Biane M. Yor Valeurs principales associées aux temps locaux browniens Bull. Sci. Math. (2) 111 1 1987 23-101
3. Csörgo, M., Horváth, L., 1993. Weighted approximations in probability and statistics. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. Wiley, Chichester. With a foreword by David Kendall.
4. C. Donati-Martin M. Yor Some Brownian functionals and their laws Ann. Probab. 25 3 1997 1011-1058
5. D'Agostino, R.B., Stephens, M.A. (Eds.), 1986. Goodness-of-fit Techniques. Statistics: Textbooks and Monographs, vol. 68, Marcel Dekker Inc., New York.
6. Durbin, J., 1973. Distribution theory for tests based on the sample distribution function. CBMS Regional Conference Series in Applied Mathematics, vol. 9, Society for Industrial and Applied Mathematics, Philadelphia.
7. Lebedev, N.N., 1972. Special Functions and their Applications (revised ed.) translated from the Russian and edited by Richard A. Silverman, Unabridged and corrected republication, Dover Publications Inc., New York.
8. J. Pitman M. Yor A decomposition of Bessel bridges Z. Wahrsch. Verw. Gebiete 59 4 1982 425-457
9. Revuz, D., Yor, M., 1999. Continuous Martingales and Brownian Motion, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 293, third ed. Springer, Berlin.
10. T. Shiga S. Watanabe Bessel diffusions as a one-parameter family of diffusion processes Z. Wahrsch. Verw. Gebiete 27 1973 37-46
11. G.R. Shorack J.A. Wellner Empirical processes with applications to statistics. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics 1986 Wiley New York
12. Yor, M., 1992. Some Aspects of Brownian Motion, Part I, Lectures in Mathematics, ETH Zürich, Birkhäuser Verlag, Basel (some special functionals).