E. O. Kantonistova, I. V. Rodionov, “On procedures for testing the equivalence of distribution tails”, Dokl. RAN. Math. Inf. Proc. Upr., 2022, Volume 507,Pages <nobr>36

MATHEMATICS

On procedures for testing the equivalence of distribution tails

E. O. Kantonistova^a, I. V. Rodionov^b

^a National Research University Higher School of Economics, Moscow, Russia
^b Institute for Information Transmission Problems (Kharkevich Institute) of the Russian Academy of Sciences, Moscow, Russia

Abstract: We propose a method for testing the hypothesis about the equivalence of the distribution tail of observed data and a certain distribution tail, which is the analogue of the goodness-of-fit hypothesis for statistics of extremes. The method is based on a new data transformation moving $k$ largest order statistics of a sample from the standard uniform distribution $U[0,1]$ to random variables asymptotically similar to a sample of size $k$ from $U[0,1]$. We prove that tests built by applying the proposed method are consistent on the widest alternative, specifically, on the negation of the null hypothesis.

Keywords: distribution tail, goodness-of-fit test, statistics of extremes, equivalence.

UDC: 519.234.3

Presented: D. A. Novikov
Received: 15.09.2022
Revised: 23.10.2022
Accepted: 30.10.2022