Related papers: On the Coverage Bound Problem of Empirical Likelih…
This paper develops a rigorous asymptotic framework for likelihood-based inference in the Block Maxima (BM) method for stationary time series. While Bayesian inference under the BM approach has been widely studied in the independence…
Confidence interval procedures used in low dimensional settings are often inappropriate for high dimensional applications. When a large number of parameters are estimated, marginal confidence intervals associated with the most significant…
Conventional likelihood-based information criteria for model selection rely on the distribution assumption of data. However, for complex data that are increasingly available in many scientific fields, the specification of their underlying…
Measurement error is a pervasive challenge across many disciplines, yet its impact on sample size determination and the accuracy and precision of estimators regarding the association between an exposure and an outcome remains understudied…
We consider the problem of guessing the realization of a random variable but under more general Tsallis' non-extensive entropic framework rather than the classical Maxwell-Boltzman-Gibbs-Shannon framework. We consider both the conditional…
In this paper we give an explicit bound on the distance to chisquare for the likelihood ratio statistic when the data are realisations of independent and identically distributed random elements. To our knowledge this is the first explicit…
The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…
We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…
Measurement error arises commonly in clinical research settings that rely on data from electronic health records or large observational cohorts. In particular, self-reported outcomes are typical in cohort studies for chronic diseases such…
We consider the problem of stochastic convex optimization with exp-concave losses using Empirical Risk Minimization in a convex class. Answering a question raised in several prior works, we provide a $O( d / n + \log( 1 / \delta) / n )$…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each edge is generated independently from a…
We develop a worst-case evaluation complexity bound for trust-region methods in the presence of unbounded Hessian approximations. We use the algorithm of arXiv:2103.15993v3 as a model, which is designed for nonsmooth regularized problems,…
In Neyman's original formulation, a 1-alpha confidence interval procedure is justified by its long-run coverage properties, and a single realized interval is to be described only by the slogan that it either covers the parameter or it does…
The local Rademacher complexity framework is one of the most successful general-purpose toolboxes for establishing sharp excess risk bounds for statistical estimators based on the framework of empirical risk minimization. Applying this…
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.…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
We advance the theory of parametric bootstrap in constructing highly efficient empirical best (EB) prediction intervals of small area means. The coverage error of such a prediction interval is of the order $O(m^{-3/2})$, where $m$ is the…
We present an optimization-based framework to construct confidence intervals for functionals in constrained inverse problems, ensuring valid one-at-a-time frequentist coverage guarantees. Our approach builds upon the now-called strict…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…