Analogues of classical goodness-of-fit tests for distribution tails
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 44-47.

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We propose analogues of the classical Kolmogorov–Smirnov and omega-squared tests for goodness-of-fit testing of distribution tails. The consistency of the proposed tests on wide alternatives is proved both in the framework of censored data statistics and in the framework of statistics of extremes.
Keywords: distribution tail, goodness-of-fit tests, type-I censoring, type-II censoring, statistics of extremes, Kolmogoro–Smirnov test, omega-squared test.
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E. O. Kantonistova; I. V. Rodionov. Analogues of classical goodness-of-fit tests for distribution tails. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 44-47. http://geodesic.mathdoc.fr/item/DANMA_2021_496_a8/

[1] Cox D.R., Oakes D., Analysis of survival data, Chapman Hall, L., N.Y., 1984, 198 pp. | MR

[2] Bücher A., Segers J., “On the maximum likelihood estimator for the generalized extreme-value distribution”, Extremes, 20 (2017), 839–872 | DOI | MR | Zbl

[3] Hosking J.R.M., Wallis J.R., Wood E.F., “Estimation of the generalized extreme-value distribution by the method of probability-weighted moments”, Technometrics, 27 (1985), 251–261 | DOI | MR

[4] Barr D.M., Davidson T., “A Kolmogorov-Smirnov test for censored samples”, Technometrics, 15 (1973), 739–757 | DOI | MR | Zbl

[5] Pettitt A.N., Stephens M.A., “Modified Cramer von Mises statistics for censored data”, Biometrika, 63 (1976), 291–298 | MR | Zbl

[6] D'Agostino R.B., Stephens M.A., Goodness of Fit Techniques, Marcel Dekker, N.Y., 1986, 576 pp. | MR | Zbl

[7] Michael J.R., Schucany W.R., “A new approach to testing goodness of fit for censored samples”, Technometrics, 21 (1979), 435–441 | DOI | Zbl

[8] Lin C.-T., Huang Y.-L., Balakrishnan N., “A New Method for Goodness-of-Fit Testing Based on Type-II Right Censored Samples”, IEEE Transactions in Reliability, 57:4 (2008), 633–642 | DOI | MR

[9] Rodionov I.V., “On discrimination between classes of distribution tails”, Problems of Information Transmission, 54 (2018), 124–138 | DOI | MR | Zbl

[10] Rodionov I.V., “On threshold selection problem for estimation of extremal index”, Proceedings of ICSM-5 (Moscow, Russia, 2021), Springer Proceedings in Mathematics and Statistics, 2021 (to appear) | MR

[11] Hüsler J., Peng L., “Review of testing issues in extremes: in honor of Professor Laurens de Haan”, Extremes, 11 (2008), 99–111 | DOI | MR | Zbl

[12] Kogut N.S., Rodionov I.V., “O kriteriyakh razlicheniya khvostov raspredelenii”, Teoriya veroyatnostei i ee primeneniya, 2021 (to appear)

[13] Chernobai A., Rachev S., Fabozzi F., “Composite goodness-of-fit tests for left-truncated loss samples”, Handbook of Financial Econometrics and Statistics, 2005, 575–596

[14] de Haan L., Ferreira A., Extreme Value Theory: An Introduction, Springer Verlag, N.Y., 2006, 417 pp. | MR | Zbl

[15] Martynov G.V., Kriterii omega-kvadrat, Nauka, M., 1978, 80 pp. | MR