arXiv subjects

Muriel Felipe Pérez-Ortiz

Publications and source records attributed to Muriel Felipe Pérez-Ortiz.

3 recordsLinked to original sources

arXiv2025

A Generalisation of Ville's Inequality to Monotonic Lower Bounds and Thresholds

Essentially all anytime-valid methods hinge on Ville's inequality to gain validity across time without incurring a union bound. Ville's inequality is a proper generalisation of Markov's inequality. It states that a non-negative supermartingale will only ever reach a multiple of its initial value with small probability. In the classic rendering both the lower bound (of zero) and the threshold are constant in time. We generalise both to monotonic curves. That is, we bound the probability that a supermartingale which remains above a given decreasing curve exceeds a given increasing threshold curve. We show our bound is tight by exhibiting a supermartingale for which the bound is an equality. Using our generalisation, we derive a clean finite-time version of the law of the iterated logarithm.

math.ST↗

arXiv2024

Anytime-Valid Tests of Group Invariance through Conformal Prediction

We develop anytime-valid tests of invariance under the action of compact groups. The resulting test statistics are optimal in a logarithmic-growth sense. We apply our method to extend recent anytime-valid tests of independence and to construct tests of normality.

stat.ME↗

arXiv2023

E-Statistics, Group Invariance and Anytime Valid Testing

We study worst-case-growth-rate-optimal (GROW) e-statistics for hypothesis testing between two group models. It is known that under a mild condition on the action of the underlying group G on the data, there exists a maximally invariant statistic. We show that among all e-statistics, invariant or not, the likelihood ratio of the maximally invariant statistic is GROW, both in the absolute and in the relative sense, and that an anytime-valid test can be based on it. The GROW e-statistic is equal to a Bayes factor with a right Haar prior on G. Our treatment avoids nonuniqueness issues that sometimes arise for such priors in Bayesian contexts. A crucial assumption on the group G is its amenability, a well-known group-theoretical condition, which holds, for instance, in scale-location families. Our results also apply to finite-dimensional linear regression.

math.ST↗