6 papers · 1 filter
Sequential testing of conditionally constrained hypotheses
Eugenio Clerico
We explicitly characterise the full class of e-processes for testing conditional non-parametric hypotheses, defined by finitely many conditional constraints. Our main result is a c…
Optimal e-values for testing the mean of a bounded random variable against a composite alternative
Sebastian Arnold, Eugenio Clerico
We derive explicitly the e-values with optimal (relative) growth rate in the worst case for testing the mean of a bounded random variable, thereby providing the first application o…
A simple geometric proof for the characterisation of e-merging functions
Eugenio Clerico
E-values offer a powerful framework for aggregating evidence across different (possibly dependent) statistical experiments. A fundamental question is to identify e-merging function…
Confidence Sequences for Generalized Linear Models via Regret Analysis
Eugenio Clerico, Hamish Flynn, Wojciech Kotłowski +1
We develop a methodology for constructing confidence sets for parameters of statistical models via a reduction to sequential prediction. Our key observation is that for any general…
Optimal e-value testing for properly constrained hypotheses
Eugenio Clerico
Hypothesis testing via e-variables can be framed as a sequential betting game, where a player each round picks an e-variable. A good player's strategy results in an effective stati…
On the optimality of coin-betting for mean estimation
Eugenio Clerico
We consider the problem of testing the mean of a bounded real random variable. We introduce a notion of optimal classes for e-variables and e-processes, and establish the optimalit…