Related papers: Asymptotic bayes optimality under sparsity for equ…
The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test…
This paper is concerned with the problem of comparing the population means of two groups of independent observations. An approximate randomization test procedure based on the test statistic of Chen and Qin (2010) is proposed. The asymptotic…
The present paper establishes new multiple procedures for simultaneous testing of a large number of hypotheses under dependence. Special attention is devoted to experiments with rare false hypotheses. This sparsity assumption is typically…
Tests of goodness of fit are used in nearly every domain where statistics is applied. One powerful and flexible approach is to sample artificial data sets that are exchangeable with the real data under the null hypothesis (but not under the…
In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…
Many sparse linear discriminant analysis (LDA) methods have been proposed to overcome the major problems of the classic LDA in high-dimensional settings. However, the asymptotic optimality results are limited to the case that there are only…
This paper considers multiple binary hypothesis tests with adaptive allocation of sensing resources from a shared budget over a small number of stages. A Bayesian formulation is provided for the multistage allocation problem of minimizing…
Randomized experiments are the gold standard for estimating the average treatment effect (ATE). While covariate adjustment can reduce the asymptotic variances of the unbiased Horvitz-Thompson estimators for the ATE, it suffers from…
Asymptotic bootstrap validity is usually understood as consistency of the distribution of a bootstrap statistic, conditional on the data, for the unconditional limit distribution of a statistic of interest. From this perspective, randomness…
Much is now known about the consistency of Bayesian updating on infinite-dimensional parameter spaces with independent or Markovian data. Necessary conditions for consistency include the prior putting enough weight on the correct…
For high-dimensional inference problems, statisticians have a number of competing interests. On the one hand, procedures should provide accurate estimation, reliable structure learning, and valid uncertainty quantification. On the other…
The advantages of adaptive experiments have led to their rapid adoption in economics, other fields, as well as among practitioners. However, adaptive experiments pose challenges for causal inference. This note suggests a BOLS (batched…
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…
The large-sample behavior of non-degenerate multivariate $U$-statistics of arbitrary degree is investigated under the assumption that their kernel depends on parameters that can be estimated consistently. Mild regularity conditions are…
The idea of an optimal test statistic in the context of simultaneous hypothesis testing was given by Sun and Tony Cai (2009) which is the conditional probability of a hypothesis being null given the data. Since we do not have a simplified…
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $\{ \mu_1, \mu_2, \mu_3\}$ through an analysis of variance…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
We propose a novel bootstrap test of a dense model, namely factor regression, against a sparse plus dense alternative augmenting model with sparse idiosyncratic components. The asymptotic properties of the test are established under time…
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…
In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of…