Nonparametric two-sample tests for increasing convex order

authored by

Ludwig Baringhaus, Rudolf Grübel

Abstract

Given two independent samples of non-negative random variables with unknown distribution functions F and G, respectively, we introduce and discuss two tests for the hypothesis that F is less than or equal to G in increasing convex order. The test statistics are based on the empirical stop-loss transform, critical values are obtained by a bootstrap procedure. It turns out that for the resampling a size switching is necessary. We show that the resulting tests are consistent against all alternatives and that they are asymptotically of the given size α. A specific feature of the problem is the behavior of the tests 'inside' the hypothesis, where F ≠ G. We also investigate and compare this aspect for the two tests.

Organisation(s)

Institute of Actuarial and Financial Mathematics

Type

Article

Journal

BERNOULLI

Volume

15

Pages

99-123

No. of pages

25

ISSN

1350-7265

Publication date

02.2009

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Statistics and Probability

Electronic version(s)

https://doi.org/10.3150/08-BEJ151 (Access: Open)