Related papers: Optimal Group-Sequential Tests with Groups of Rand…
This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple…
We consider the problem of simultaneous detection and estimation under a sequential framework. In particular we are interested in sequential tests that distinguish between the null and the alternative hypothesis and every time the decision…
Group sequential designs drive innovation in clinical, industrial, and corporate settings. Early stopping for failure in sequential designs conserves experimental resources, whereas early stopping for success accelerates access to improved…
A family of variable stage size multistage tests of simple hypotheses is described, based on efficient multistage sampling procedures. Using a loss function that is a linear combination of sampling costs and error probabilities, these tests…
Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the…
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,…
Recent years have seen tremendous advances in the theory and application of sequential experiments. While these experiments are not always designed with hypothesis testing in mind, researchers may still be interested in performing tests…
In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…
We present a general framework for hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of…
Let $X_1,X_2,...$ be a discrete-time stochastic process with a distribution $P_\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. We consider the problem of testing a simple hypothesis $H_0:$ $\theta=\theta_0$…
This article reviews a class of adaptive group testing procedures that operate under a probabilistic model assumption as follows. Consider a set of $N$ items, where item $i$ has the probability $p$ ($p_i$ in the generalized group testing)…
While many statistical procedures rely on a fixed sample size, sequential methods allow a decision-maker to adapt the sample size to achieve a given precision. In this way, sequential tests reduce the average number of observations required…
This paper addresses the following general scenario: A scientist wishes to perform a battery of experiments, each generating a sequential stream of data, to investigate some phenomenon. The scientist would like to control the overall error…
Likelihood methods for measuring statistical evidence obey the likelihood principle while maintaining bounded and well-controlled frequency properties. These methods lend themselves to sequential study designs because they measure the…
A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample…
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…
In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the…
In this paper, we develop a simple approach for testing multiple statistical hypotheses based on the observations of a number of probability ratios enumerated consecutively with respect to the index of hypotheses. Explicit and tight bounds…
A popular setting in medical statistics is a group sequential trial with independent and identically distributed normal outcomes, in which interim analyses of the sum of the outcomes are performed. Based on a prescribed stopping rule, one…
The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…