Details
| Original language | English |
|---|---|
| Pages (from-to) | 99-123 |
| Number of pages | 25 |
| Journal | BERNOULLI |
| Volume | 15 |
| Issue number | 1 |
| Publication status | Published - Feb 2009 |
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.
Keywords
- Bootstrap critical values, Empirical stop-loss transform, Increasing convex order, One-sided two-sample tests
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
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In: BERNOULLI, Vol. 15, No. 1, 02.2009, p. 99-123.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Nonparametric two-sample tests for increasing convex order
AU - Baringhaus, Ludwig
AU - Grübel, Rudolf
PY - 2009/2
Y1 - 2009/2
N2 - 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.
AB - 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.
KW - Bootstrap critical values
KW - Empirical stop-loss transform
KW - Increasing convex order
KW - One-sided two-sample tests
UR - http://www.scopus.com/inward/record.url?scp=62749172413&partnerID=8YFLogxK
U2 - 10.3150/08-BEJ151
DO - 10.3150/08-BEJ151
M3 - Article
AN - SCOPUS:62749172413
VL - 15
SP - 99
EP - 123
JO - BERNOULLI
JF - BERNOULLI
SN - 1350-7265
IS - 1
ER -