Testing for tail behavior using extreme spacings

TL;DR

This paper introduces new statistical tests for assessing the tail-heaviness of distributions based on extreme spacings, demonstrating their robustness, good error control, and increased power when data is blocked.

Contribution

It presents novel tail behavior tests using extreme spacings that are consistent, robust, and outperform some existing methods, especially with blocked data.

Findings

Tests control Type I error well

Power increases with data blocking

Compared favorably with Bryson's test

Abstract

Methodologies to test hypotheses about the tail-heaviness of an underlying distribution are introduced based on results of Rojo (1996) using the limiting behavior of the extreme spacings. The tests are consistent and have point-wise robust levels in the sense of Lehmann (2005) and Lehmann and Loh (1990). Simulation results based on these new methodologies indicate that the tests exhibit good control of the probability of Type I error and have good power properties for finite sample sizes. The tests are compared with a test proposed by Bryson (1974) and it is seen that, although Bryson's test is competitive with the tests proposed here, Bryson's test does not have point-wise robust levels. The operating characteristics of the tests are also explored when the data is blocked. It turns out that the power increases substantially by blocking. The methodology is illustrated by analyzing various data sets.