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A Likelihood-Ratio Test for Verifying Weak Stochastic Transitivity
Abstract
This paper proposes and studies a likelihood-ratio test of the null hypothesis that weak stochastic transitivity (WST) does not hold. This is the reverse of the formulation commonly used in the literature, where WST is set as the null hypothesis. We show that, even when the number of items grows with the number of comparisons per pair, the uniform size converges to the nominal level, with the critical value determined by a chi-bar-square distribution. We further establish that the Type II error converges uniformly to zero under a sufficient signal-strength condition. Simulation studies demonstrate good finite-sample Type I error control and show that power increases with the sample size and signal strength.
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BibTeX
@misc{toyoda2026likelihoodratio,
title = {{A Likelihood-Ratio Test for Verifying Weak Stochastic Transitivity}},
author = {Masaki Toyoda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06608},
eprint = {2609.06608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06608},
}
RIS
TY - UNPB
TI - A Likelihood-Ratio Test for Verifying Weak Stochastic Transitivity
AU - Masaki Toyoda
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06608
UR - https://arxiv.org/abs/2609.06608
AB - This paper proposes and studies a likelihood-ratio test of the null hypothesis that weak stochastic transitivity (WST) does not hold. This is the reverse of the formulation commonly used in the literature, where WST is set as the null hypothesis. We show that, even when the number of items grows with the number of comparisons per pair, the uniform size converges to the nominal level, with the critical value determined by a chi-bar-square distribution. We further establish that the Type II error converges uniformly to zero under a sufficient signal-strength condition. Simulation studies demonstrate good finite-sample Type I error control and show that power increases with the sample size and signal strength.
ER -