Abstract
The uniform distance between the distribution functions of the von Mises ω2-statistic for sampling from a continuous distribution and of the "generalized Bayesian ω2-statistic" for sampling from the uniform distribution on a finite number of points is estimated. Application to the generalized Bayesian bootstraps is discussed.
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REFERENCES
Götze, F. (1979). Asymptotic expansions for bivariate von Mises functionals, Z. Wahrsch. Verw. Gebiete., 50, 333–355.
Korolyuk, V. S. and Borovskikh, Yu. V. (1984). Asymptotic Analysis of Distributions of Statistics, Naukova Dumka, Kiev.
Lo, A. Y. (1987). A large sample study of the Bayesian bootstrap, Ann. Statist., 15, 360–375.
Lo, A. Y. (1991). Bayesian bootstrap clones and a blometry function, Sankhyā Ser. A, 53, 320–333.
Lo, A. Y. and Sazonov, V. V. (1995). On the closeness of von Mises ω 2-statistics and their bootstrap approximations, Theory Probab. Appl., 40, 850–858.
Paulauskas, V. and Rackauskas, A. (1989). Approximation Theory in the Central Limit Theorem. Exact Results in Banach Spaces, Kluwer, Dordrecht.
Petrov, V. V. (1975). Sums of Independent Random Variables, Springer, Berlin.
Sazonov, V. V., Ulyanov, V. V. and Zalesskii, B. A. (1988). Normal approximation in Hilbert space I, Theory Probab. Appl., 33, 207–227.
Ulyanov, V. V. (1987). Asymptotic expansions for distributions of sums of independent random variables in H, Theory Probab. Appl., 31, 25–39.
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Lo, A.Y., Sazonov, V.V. Von Mises ω2-Statistic and the generalized Bayesian Bootstraps. Annals of the Institute of Statistical Mathematics 49, 25–34 (1997). https://doi.org/10.1023/A:1003106504422
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DOI: https://doi.org/10.1023/A:1003106504422