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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 40, Fasc. 2,
pages 331 - 348
DOI: 10.37190/0208-4147.40.2.8
Published online 10.8.2020
 

Intermediate efficiency of tests under heavy-tailed alternatives

Tadeusz Inglot

Abstract: 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.

2010 AMS Mathematics Subject Classification: Primary 62G10; Secondary 62G20, 60F10.

Keywords and phrases: asymptotic relative efficiency, intermediate efficiency, goodness-of-fit test, Kolmogorov--Smirnov test, Neyman--Pearson test, local alternatives, heavy-tailed alternatives, square integrable alternatives.

References


[1] B. Ɔmiel, T. Inglot and T. Ledwina, Intermediate efficiency of some weighted goodness-of-fit statistics, J. Nonparametric Statist. (online, 2020).

[2] Ermakov, M. S. (2004). On asymptotically efficient statistical inference for moderate deviation probabilities, Theory Probab. Appl. , 622-641.

[3] Inglot, T. (1999). Generalized intermediate efficiency of goodness of fit tests, Math. Methods Statist. , 487-509.

[4] Inglot, T., and Ledwina, T. (1990). On probabilities of excessive deviations for Kolmogorov-Smirnov, Cramér- von Mises and chi-square statistics, Ann. Statist. , 1491-1495.

[5] Inglot, T., and Ledwina, T. (1996). Asymptotic optimality of data driven Neyman's tests for uniformity, Ann. Statist. , 1982-2019.

[6] Inglot, T., and Ledwina, T. (2001). Intermediate approach to comparison of some goodness-of-fit tests, Ann. Inst. Statist. Math. , 810-834.

[7] Inglot, T., and Ledwina, T. (2006). Intermediate efficiency of some max-type statistics, J. Statist. Plan. Inference , 2918-2935.

[8] Inglot, T., Ledwina, T., and Ćmiel, B. (2019). Intermediate efficiency in some nonparametric testing problems with an application to some weighted statistics, ESAIM Probab. Statist. , 697-738.

[9] Kallenberg, W. C. M. (1983). Intermediate efficiency, theory and examples, Ann. Statist. , 1401-1420.

[10] Mason, D. M., and Eubank, R. L. (2012). Moderate deviations and intermediate efficiency for lack-of-fit tests, Statistics Risk Modeling , 175-187.

[11] Mirakhmedov, S. M. (2019). Asymptotic intermediate efficiency of the chi-square and likelihood ratio goodness of fit tests, arXiv:1610.04135v3 .

[12] Yurinskii, V. V. (1976). Exponential inequalities for sums of random vectors, J. Multivariate Anal. , 473-499.

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