Related papers: Optimal Decision Rules for Simple Hypothesis Testi…
Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…
Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the…
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…
We study the Neyman-Pearson problem for convex expectations on L^{\infty}(\mu). The existence of the optimal test is given. Without assuming that the level sets of penalty functions are weakly compact, we prove that the optimal tests for…
We propose and study a general method for construction of consistent statistical tests on the basis of possibly indirect, corrupted, or partially available observations. The class of tests devised in the paper contains Neyman's smooth…
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 statistical test that rejects the null hypothesis as soon as…
In this paper, we are interested in heuristic parameter choice rules for general convex variational regularization which are based on error estimates. Two such rules are derived and generalize those from quadratic regularization, namely the…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
When dealing with the problem of simultaneously testing a large number of null hypotheses, a natural testing strategy is to first reduce the number of tested hypotheses by some selection (screening or filtering) process, and then to…
This paper studies optimal decision rules, including estimators and tests, for weakly identified GMM models. We derive the limit experiment for weakly identified GMM, and propose a theoretically-motivated class of priors which give rise to…
In this paper, our interest is in the problem of simultaneous hypothesis testing when the test statistics corresponding to the individual hypotheses are possibly correlated. Specifically, we consider the case when the test statistics…
The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…
The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…
We study the Neyman-Pearson theory for convex expectations (convex risk measures) on $L^{\infty}(\mu)$. Without assuming that the level sets of penalty functions are weakly compact, a new approach different from the convex duality method is…
We consider a problem of simple hypothesis testing using a randomized test via a tunable loss function proposed by Liao \textit{et al}. In this problem, we derive results that correspond to the Neyman--Pearson lemma, the Chernoff--Stein…
A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions for a class of statistical decision problems. In particular, we are interested in…
The problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings. In the fixed sample size setting, for binary hypothesis testing, the optimal exponent for the maximal error…
We point out that the Neyman-Pearson lemma applies to Bayes factors if we consider expected type-1 and type-2 error rates. That is, the Bayes factor is the test statistic that maximises the expected power for a fixed expected type-1 error…
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is…
We apply classical statistical decision theory to a large class of treatment choice problems with partial identification. We show that, in a general class of problems with Gaussian likelihood, all decision rules are admissible; it is…