Related papers: Adaptive multigroup confidence intervals with cons…
Confidence intervals (CIs) are instrumental in statistical analysis, providing a range estimate of the parameters. In modern statistics, selective inference is common, where only certain parameters are highlighted. However, this selective…
We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…
Multivariate meta-analysis is gaining prominence in evidence synthesis research because it enables simultaneous synthesis of multiple correlated outcome data, and random-effects models have generally been used for addressing between-studies…
We consider interval estimation of the difference between two binomial proportions. Several methods of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly…
Bootstrap is a widely used technique that allows estimating the properties of a given estimator, such as its bias and standard error. In this paper, we evaluate and compare five bootstrap-based methods for making confidence intervals: two…
Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We…
We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an empirical Bayes method. Next we consider a central set of…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
Adaptive experiment designs can dramatically improve statistical efficiency in randomized trials, but they also complicate statistical inference. For example, it is now well known that the sample mean is biased in adaptive trials.…
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…
Standard confidence intervals employed in applied statistical analysis are usually based on asymptotic approximations. Such approximations can be considerably inaccurate in small and moderate sized samples. We derive accurate confidence…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high dimensional linear regression with random design. We first establish the convergence rates of the minimax expected…
We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain…
We consider the classic problem of interval estimation of a proportion $p$ based on binomial sampling. The "exact" Clopper-Pearson confidence interval for $p$ is known to be unnecessarily conservative. We propose coverage-adjustments of the…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
Conformal prediction is a popular method to construct prediction intervals with marginal coverage guarantees from black-box machine learning models. In applications with potentially high-impact events, such as flooding or financial crises,…
Confidence intervals are assessed according to two criteria, namely expected length and coverage probability. In an attempt to apply the decision-theoretic method to finding a good confidence interval, a loss function that is a linear…
This paper revisits the simple, but empirically salient, problem of inference on a real-valued parameter that is partially identified through upper and lower bounds with asymptotically normal estimators. A simple confidence interval is…
The following questions are discussed: ``Why confidence intervals are a hot topic?''; ``Are confidence intervals objective?''; ``What is the usefulness of coverage?''; ``How to obtain useful information from experiment?''; ``The confidence…