Related papers: Hypothesis Testing with the General Source
Many scientific applications involve testing theories that are only partially specified. This task often amounts to testing the goodness-of-fit of a candidate distribution while allowing for reasonable deviations from it. The tolerant…
The generalized quantum Stein's lemma characterizes the optimal asymptotic exponent of the type-II error in quantum hypothesis testing for an independent and identically distributed (IID) null hypothesis against a composite alternative…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
Practical problems with missing data are common, and statistical methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism…
The extraction of nonstationary signals from blind and semi-blind multivariate observations is a recurrent problem. Numerous algorithms have been developed for this problem, which are based on the exact or approximate joint diagonalization…
We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization…
We propose a general framework for constructing powerful, sequential hypothesis tests for a large class of nonparametric testing problems. The null hypothesis for these problems is defined in an abstract form using the action of two known…
Testing to see whether a given data set comes from some specified distribution is among the oldest types of problems in Statistics. Many such tests have been developed and their performance studied. The general result has been that while a…
In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states…
We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take…
This article deals with the hypothesis test for the extremely heavy-tailed distributions with infinite mean or variance by using a truncated sample mean. We obtain three necessary and sufficient conditions under which the asymptotic…
The achievable error-exponent pairs for the type I and type II errors are characterized in a hypothesis testing setup where the observation consists of independent and identically distributed samples from either a known joint probability…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
Statistical hypothesis tests typically use prespecified sample sizes, yet data often arrive sequentially. Interim analyses invalidate classical error guarantees, while existing sequential methods require rigid testing preschedules or incur…
Null Hypothesis Significance Testing (NHST) has long been of central importance to psychology as a science, guiding theory development and underlying the application of evidence-based intervention and decision-making. Recent years, however,…
The network data has attracted considerable attention in modern statistics. In research on complex network data, one key issue is finding its underlying connection structure given a network sample. The methods that have been proposed in…
Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…