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Concentration inequalities for the sample mean, like those due to Bernstein, Hoeffding, and Bentkus, are valid for any sample size but overly conservative, yielding confidence intervals that are unnecessarily wide. The central limit theorem…

Probability · Mathematics 2025-12-23 Morgane Austern , Lester Mackey

Introduction: estimation of confidence intervals (CIs) of binomial proportions has been reviewed more than once but the directional interpretation, distinguishing the overestimation from the underestimation, was neglected while the sample…

Other Statistics · Statistics 2021-03-22 André Gillibert , Jacques Bénichou , Bruno Falissard

Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics…

Statistics Theory · Mathematics 2022-11-08 Amichai Painsky

A confidence sequence is a sequence of confidence intervals that is uniformly valid over an unbounded time horizon. Our work develops confidence sequences whose widths go to zero, with nonasymptotic coverage guarantees under nonparametric…

Statistics Theory · Mathematics 2022-08-09 Steven R. Howard , Aaditya Ramdas , Jon McAuliffe , Jasjeet Sekhon

Randomized quasi-Monte Carlo (RQMC) methods estimate the mean of a random variable by sampling an integrand at $n$ equidistributed points. For scrambled digital nets, the resulting variance is typically $\tilde O(n^{-\theta})$ where…

Numerical Analysis · Mathematics 2026-02-03 Aadit Jain , Fred J. Hickernell , Art B. Owen , Aleksei G. Sorokin

We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional…

Applications · Statistics 2022-10-04 Timothy B. Armstrong , Michal Kolesár

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…

Statistics Theory · Mathematics 2023-01-03 Lang Liu , Zaid Harchaoui

There are over 55 different ways to construct a confidence respectively credible interval (CI) for the binomial proportion. Methods to compare them are necessary to decide which should be used in practice. The interval score has been…

Methodology · Statistics 2022-07-08 Lisa J. Hofer , Leonhard Held

We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…

Statistics Theory · Mathematics 2020-11-05 Erik Learned-Miller , Philip S. Thomas

Any supervised machine learning analysis is required to provide an estimate of the out-of-sample predictive performance. However, it is imperative to also provide a quantification of the uncertainty of this performance in the form of a…

Machine Learning · Computer Science 2024-06-13 Konstantinos Paraschakis , Andrea Castellani , Giorgos Borboudakis , Ioannis Tsamardinos

When assessing the quality of prediction models in machine learning, confidence intervals (CIs) for the generalization error, which measures predictive performance, are a crucial tool. Luckily, there exist many methods for computing such…

We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…

Methodology · Statistics 2026-05-11 Tim Ritmeester

A confidence sequence (CS) is a sequence of confidence intervals that is valid at arbitrary data-dependent stopping times. These are useful in applications like A/B testing, multi-armed bandits, off-policy evaluation, election auditing,…

Statistics Theory · Mathematics 2024-02-09 Hongjian Wang , Aaditya Ramdas

Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…

Machine Learning · Statistics 2026-05-12 Valentin Kilian , Stefano Cortinovis , François Caron

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…

Statistics Theory · Mathematics 2020-11-24 Morgane Austern , Vasilis Syrgkanis

We consider inference on a scalar regression coefficient under a constraint on the magnitude of the control coefficients. A class of estimators based on a regularized propensity score regression is shown to exactly solve a tradeoff between…

Econometrics · Economics 2023-08-11 Timothy B. Armstrong , Michal Kolesár , Soonwoo Kwon

We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The intervals are centered at the usual linear empirical Bayes estimator, but use a critical value accounting for shrinkage. Parametric EBCIs that…

Econometrics · Economics 2022-11-22 Timothy B. Armstrong , Michal Kolesár , Mikkel Plagborg-Møller

This paper introduces Conformal Thresholded Intervals (CTI), a novel conformal regression method that aims to produce the smallest possible prediction set with guaranteed coverage. Unlike existing methods that rely on nested conformal…

Machine Learning · Computer Science 2025-01-03 Rui Luo , Zhixin Zhou

Multi-arm bandit experimental designs are increasingly being adopted over standard randomized trials due to their potential to improve outcomes for study participants, enable faster identification of the best-performing options, and/or…

Methodology · Statistics 2025-06-04 Brian M Cho , Aurélien Bibaut , Nathan Kallus

What, if anything, should a frequentist say about a single realized confidence interval (CI) and its chance of having covered the parameter? Jerzy Neyman's original answer was to refuse any nondegenerate probability for coverage ex post…

Other Statistics · Statistics 2026-03-06 Scott Lee