Related papers: Optimal tests following sequential experiments
It has been recently shown that e-processes are sufficient for sequential testing in the following sense: every level-$\alpha$ sequential test can be obtained by thresholding an e-process at $1/\alpha$. However, in the above result, neither…
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…
The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…
The problem of simultaneously testing the marginal distributions of sequentially monitored, independent data streams is considered. The decisions for the various testing problems can be made at different times, using data from all streams,…
This article develops a method to construct the optimal sequential test for monitoring the changes in the distribution of finite observation sequences with a general dependence structure. This method allows us to prove that different…
This paper studies optimal hypothesis testing for nonregular econometric models with parameter-dependent support. We consider both one-sided and two-sided hypothesis testing and develop asymptotically uniformly most powerful tests based on…
In this paper we consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X_1,..., X_n are i.i.d. with distribution P_{\theta}, with \theta \in R^k. Let g(\theta) be some real-valued parameter of interest.…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
After a brief review of recent advances in sequential analysis involving sequential generalized likelihood ratio tests, we discuss their use in psychometric testing and extend the asymptotic optimality theory of these sequential tests to…
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and…
Sequential tests and their implied confidence sequences, which are valid at arbitrary stopping times, promise flexible statistical inference and on-the-fly decision making. However, strong guarantees are limited to parametric sequential…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
This article develops a continuous-time asymptotic framework for analyzing adaptive experiments -- settings in which data collection and treatment assignment evolve dynamically in response to incoming information. A key challenge in…
This paper provides a statistical method to test whether a system that performs a binary sequential hypothesis test is optimal in the sense of minimizing the average decision times while taking decisions with given reliabilities. The…
The main purpose of this paper is to provide an asymptotically optimal test. The proposed statistic is of Neyman-Pearson-type when the parameters are estimated with a particular kind of estimators. It is shown that the proposed estimators…
We consider sequential hypothesis testing based on observations which are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent…
Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one…