On Probabilities of Excessive Deviations for Kolmogorov-Smirnov, Cramer-von Mises and Chi-Square Statistics

Inglot, Tadeusz; Ledwina, Teresa

Ann. Statist., Tome 18 (1990) no. 1, p. 1491-1495 / Harvested from Project Euclid

Résumé

Let $\alpha_n$ be the classical empirical process and $T: D\lbrack 0, 1\rbrack \rightarrow R$. Assume $T$ satisfies the Lipschitz condition. Using the Komlos-Major-Tusnady inequality, bounds for $P(T(\alpha_n) \geq x_n \sqrt n)$ are obtained for every $n$ and $x_n > 0$. Hence expansions for large deviations, as well as some moderate and Cramer-type large-deviations results for $T(\alpha_n)$, are derived.

Publié le : 1990-09-14
Classification: Excessive deviations, large deviations, moderate deviations, Cramer-type deviations, strong approximation, Cramer-von Mises test, Kolmogorov-Smirnov test, chi-square test, Neyman's test, quadratic statistics, 60F10, 62G20, 62E20, 62E15

@article{1176347764,
     author = {Inglot, Tadeusz and Ledwina, Teresa},
     title = {On Probabilities of Excessive Deviations for Kolmogorov-Smirnov, Cramer-von Mises and Chi-Square Statistics},
     journal = {Ann. Statist.},
     volume = {18},
     number = {1},
     year = {1990},
     pages = { 1491-1495},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176347764}
}

Inglot, Tadeusz; Ledwina, Teresa. On Probabilities of Excessive Deviations for Kolmogorov-Smirnov, Cramer-von Mises and Chi-Square Statistics. Ann. Statist., Tome 18 (1990) no. 1, pp.  1491-1495. http://gdmltest.u-ga.fr/item/1176347764/