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.
We study the computational complexity of hypothesis testing in the spiked Wigner model, a prototypical model for detecting low-rank structure in a large random matrix. Below the"BBP"eigenvalue transition, it is expected that strong detection --- with both type I and II errors vanishing --- requires exponential time. As...
A simple decomposition of a neural-network-based normalizing flow that naturally uncovers a pivotal statistic in the presence of nuisance parameters, based only on a sample generator from the distribution of interest is presented.
In safe hypothesis testing with test supermartingals, Ville's inequality provides anytime-valid type-I error guarantees for every significance level $\alpha\in(0,1]$, if one rejects the null hypothesis whenever the wealth process first exceeds $\frac{1}{\alpha}$. Due to an inherent asymmetry, the type-II error does not...
We introduce a distribution-free goodness-of-fit test, termed the omega-1 test, which naturally complements the Kolmogorov--Smirnov test and Cram\'{e}r--von Mises test and can be viewed as their (piecewise) linear analog. Defined as an $\mathrm{L}^{1}$-functional of the empirical process, the test statistic improves on...
Many economic applications establish stability of Markov dynamics using the monotone mixing condition (MMC) of Hopenhayn and Prescott (1992). Working in the same setting as that paper, we introduce a weak monotone mixing condition (WMMC), phrased in terms of the reversal of rank between populations, and show that it is...
Takashi Kamihigashi, Qing-Yin Ma, J. Stachurski· 0 citations
We present an approach for determining sample sizes required to detect underestimations of the expected shortfall with a prescribed power when applying the recently proposed e-backtesting procedure. We consider scenarios in which the value-at-risk at level $p$ is always estimated correctly, while the difference between...
Dennis Oestmann, T. Dickhaus· 0 citations
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