Related papers: Power comparison of sequential testing by betting …
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
Experimentation involves risk. The investigator expends time and money in the pursuit of data that supports a hypothesis. In the end, the investigator may find that all of these costs were for naught and the data fail to reject the null.…
Testing differences in mean vectors is a fundamental task in the analysis of high-dimensional compositional data. Existing methods may suffer from low power if the underlying signal pattern is in a situation that does not favor the deployed…
When permutation methods are used in practice, often a limited number of random permutations are used to decrease the computational burden. However, most theoretical literature assumes that the whole permutation group is used, and methods…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
On observing a sequence of i.i.d.\ data with distribution $P$ on $\mathbb{R}^d$, we ask the question of how one can test the null hypothesis that $P$ has a log-concave density. This paper proves one interesting negative and positive result:…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
Equivalence tests, otherwise known as parity or similarity tests, are frequently used in ``bioequivalence studies" to establish practical equivalence rather than the usual statistical significant difference. In this article, we propose an…
We introduce a method for proving almost sure termination in the context of lambda calculus with continuous random sampling and explicit recursion, based on ranking supermartingales. This result is extended in three ways. Antitone ranking…
In any parametric inference problem, the robustness of the procedure is a real concern. A procedure which retains a high degree of efficiency under the model and simultaneously provides stable inference under data contamination is…
We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
We describe group sequential tests which efficiently incorporate information from multiple endpoints allowing for early stopping at pre-planned interim analyses. We formulate a testing procedure where several outcomes are examined, and…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…
Consider two forecasters, each making a single prediction for a sequence of events over time. We ask a relatively basic question: how might we compare these forecasters, either online or post-hoc, while avoiding unverifiable assumptions on…
We connect the power of Confidence Intervals in different Frequentist methods to their reliability. We show that in the case of a bounded parameter a biased method which near the boundary has large power in testing the parameter against…
We consider the power to reject false values of the parameter in Frequentist methods for the calculation of confidence intervals. We connect the power with the physical significance (reliability) of confidence intervals for a parameter…
We introduce a simple tool to control for false discoveries and identify individual signals in scenarios involving many tests, dependent test statistics, and potentially sparse signals. The tool applies the Cauchy combination test…
We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover,…