Related papers: Almost optimal sequential tests of discrete compos…
We present a robust test for composite null hypothesis based on the general $S$-divergence family. This requires a non-trivial extension of the results of Ghosh et al.~(2015). We derive the asymptotic and theoretical robustness properties…
The problem of multi-hypothesis testing with controlled sensing of observations is considered. The distribution of observations collected under each control is assumed to follow a single-parameter exponential family distribution. The goal…
We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…
A variety of statistics based on sample spacings has been studied in the literature for testing goodness-of-fit to parametric distributions. To test the goodness-of-fit to a nonparametric class of univariate shape-constrained densities,…
We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected…
The indirect effect of an exposure on an outcome through an intermediate variable can be identified by a product of two regression coefficients under certain causal and regression modeling assumptions. In this context, the null hypothesis…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
In multiple classification, one aims to determine whether a testing sequence is generated from the same distribution as one of the M training sequences or not. Unlike most of existing studies that focus on discrete-valued sequences with…
Consider a finite set of sources, each producing i.i.d. observations that follow a unique probability distribution on a finite alphabet. We study the problem of matching a finite set of observed sequences to the set of sources under the…
This study derives a new property of the Wishart distribution when the degree-of-freedom and the size of the matrix parameter of the distribution grow simultaneoulsy. Particularly, the asymptotic normality of the product of four independent…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test…
A/B testing refers to the task of determining the best option among two alternatives that yield random outcomes. We provide distribution-dependent lower bounds for the performance of A/B testing that improve over the results currently…
In the classical two-sample problem, the conventional approach for testing distributions equality is based on the difference between the two marginal empirical distribution functions, whereas a test for independence is based on the contrast…
We study the likelihood ratio test in general mixture models where the base density is parametric, the null is a known fixed mixing distribution, and the alternative is a general mixing distribution supported on a bounded parameter space.…
In this paper we revisit the binary hypothesis testing problem with one-sided compression. Specifically we assume that the distribution in the null hypothesis is a mixture distribution of iid components. The distribution under the…
We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
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…