Intermediate Efficiency of Tests Under Heavy-Tailed Alternatives

• Autorzy: Inglot Tadeusz

Identyfikatory

DOI

10.37190/0208-4147.40.2.8

• Języki publikacji: EN

Abstrakty

EN

We show that for local alternatives which are not square integrable the intermediate (or Kallenberg) efficiency of the Neyman–Pearson test for uniformity with respect to the classical Kolmogorov–Smirnov test is infinite. By contrast, for square integrable local alternatives the intermediate efficiency is finite and can be explicitly calculated.

Słowa kluczowe

EN

asymptotic relative efficiency; intermediate efficiency; goodness-of-fit test; Kolmogorov–Smirnov test; Neyman–Pearson test; local alternatives; heavy-tailed alternatives; square integrable alternatives

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2020
• Tom: Vol. 40, Fasc. 2
• Strony: 331--348
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Inglot Tadeusz

• Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

• [1] B. Ćmiel, T. Inglot and T. Ledwina, Intermediate efficiency of some weighted goodness-of-fit statistics, J. Nonparametric Statist. (online, 2020).
• [2] M. S. Ermakov, On asymptotically efficient statistical inference for moderate deviation probabilities, Theory Probab. Appl. 48 (2004), 622-641.
• [3] T. Inglot, Generalized intermediate efficiency of goodness of fit tests, Math. Methods Statist. 8 (1999), 487-509.
• [4] T. Inglot and T. Ledwina, On probabilities of excessive deviations for Kolmogorov-Smirnov, Cramér-von Mises and chi-square statistics, Ann. Statist. 18 (1990), 1491-1495.
• [5] T. Inglot and T. Ledwina, Asymptotic optimality of data driven Neyman’s tests for uniformity, Ann. Statist. 24 (1996), 1982-2019.
• [6] T. Inglot and T. Ledwina, Intermediate approach to comparison of some goodness-of-fit tests, Ann. Inst. Statist. Math. 53 (2001), 810-834.
• [7] T. Inglot and T. Ledwina, Intermediate efficiency of some max-type statistics, J. Statist. Plan. Inference 136 (2006), 2918-2935.
• [8] T. Inglot, T. Ledwina and B. Ćmiel, Intermediate efficiency in some nonparametric testing problems with an application to some weighted statistics, ESAIM Probab. Statist. 23 (2019), 697-738.
• [9] W. C. M. Kallenberg, Intermediate efficiency, theory and examples, Ann. Statist. 11 (1983), 1401-1420.
• [10] D. M. Mason and R. L. Eubank, Moderate deviations and intermediate efficiency for lack-of-fit tests, Statistics Risk Modeling 29 (2012), 175-187.
• [11] S. M. Mirakhmedov, Asymptotic intermediate efficiency of the chi-square and likelihood ratio goodness of fit tests, arXiv:1610.04135v3 (2019).
• [12] V. V. Yurinskii, Exponential inequalities for sums of random vectors, J. Multivariate Anal. 6 (1976), 473-499.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).