相关论文: Te Test: A New Non-asymptotic T-test for Behrens-F…

Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$-th draw? This is a classical problem in statistics,…

This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…

Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…

The development of statistical methods for valid and efficient probabilistic inference without prior distributions has a long history. Fisher's fiducial inference is perhaps the most famous of these attempts. We argue that, despite its…

The $k$-means is one of the most important unsupervised learning techniques in statistics and computer science. The goal is to partition a data set into many clusters, such that observations within clusters are the most homogeneous and…

We consider a Bayesian framework for estimating the sample size of a clinical trial. The new approach, called BESS, is built upon three pillars: Sample size of the trial, Evidence from the observed data, and Confidence of the final decision…

Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton…

In many situations, when dealing with several populations, equality of the covariance operators is assumed. An important issue is to study if this assumption holds before making other inferences. In this paper, we develop a test for…

After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…

We study the normal mean inference problem, which involves simultaneous testing of the means of many normal distributions. This problem has been extensively studied within the empirical Bayes (EB) framework. However, the reliability of most…

In this paper, we focus on testing multivariate normality using the BHEP test with data that are missing completely at random. Our objective is twofold: first, to gain insight into the asymptotic behavior of BHEP test statistics under two…

There is a growing trend among statistical agencies to explore non-probability data sources for producing more timely and detailed statistics, while reducing costs and respondent burden. Coverage and measurement error are two issues that…

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

The two-sample homogeneity testing problem is fundamental in statistics and becomes particularly challenging in high dimensions, where classical tests can suffer substantial power loss. We develop a learning-assisted procedure based on the…

Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…

A unified family of goodness-of-fit tests based on $\phi$-divergences is introduced and studied. The new family of test statistics $S_n(s)$ includes both the supremum version of the Anderson--Darling statistic and the test statistic of Berk…

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…

Ever since the proof of asymptotic normality of maximum likelihood estimator by Cramer (1946), it has been understood that a basic technique of the Taylor series expansion suffices for asymptotics of $M$-estimators with…

In this article, we introduce a novel discrepancy called the maximum variance discrepancy for the purpose of measuring the difference between two distributions in Hilbert spaces that cannot be found via the maximum mean discrepancy. We also…

Given a stream of Bernoulli random variables, consider the problem of estimating the mean of the random variable within a specified relative error with a specified probability of failure. Until now, the Gamma Bernoulli Approximation Scheme…