Nonparametric two-sample tests for increasing convex order

Details Nonparametric two-sample tests for increasing convex order Nonparametric two-sample tests for increasing convex order

2009-02-09

arxiv.org/abs/0902.1439v1

Bernoulli 2009, Vol. 15, No. 1, 99-123

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ151 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ151

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 $\alpha$. A specific feature of the problem is the behavior of the tests `inside' the hypothesis, where $F\not=G$. We also investigate and compare this aspect for the two tests.

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