Related papers: Exact adaptive confidence intervals for small area…

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…

Constructing distribution-free confidence intervals for the median, a classic problem in statistics, has seen numerous solutions in the literature. While coverage validity has received ample attention, less has been explored about interval…

Classically, confidence intervals are required to have consistent coverage across all values of the parameter. However, this will inevitably break down if the underlying estimation procedure is biased. For this reason, many efforts have…

Meta-analysis can be formulated as combining $p$-values across studies into a joint $p$-value function, from which point estimates and confidence intervals can be derived. We extend the meta-analytic estimation framework based on combined…

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…

Empirical Bayes small area estimation based on the well-known Fay-Herriot model may produce unreliable estimates when outlying areas exist. Existing robust methods against outliers or model misspecification are generally inefficient when…

In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…

Well-recommended methods of forming `confidence intervals' for a binomial proportion give interval estimates that do not actually meet the definition of a confidence interval, in that their coverages are sometimes lower than the nominal…

In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…

In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a…

Prediction intervals are commonly used in meta-analysis with random-effects models. One widely used method, the Higgins-Thompson-Spiegelhalter prediction interval, replaces the heterogeneity parameter with its point estimate, but its…

We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection…

Classical confidence intervals after best subset selection are widely implemented in statistical software and are routinely used to guide practitioners in scientific fields to conclude significance. However, there are increasing concerns in…

This paper develops conformal inference methods to construct a confidence interval for the frequency of a queried object in a very large discrete data set, based on a sketch with a lower memory footprint. This approach requires no knowledge…

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…

We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…

Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in…

Objectives: Estimation of areas under receiver operating characteristic curves (AUCs) and their differences is a key task in diagnostic studies. We aimed to derive, evaluate, and implement simple sample size formulas for such studies with a…

Several uncertainty estimation methods have been recently proposed for machine translation evaluation. While these methods can provide a useful indication of when not to trust model predictions, we show in this paper that the majority of…

We propose an adaptive confidence interval procedure (CIP) for the coefficients in the normal linear regression model. This procedure has a frequentist coverage rate that is constant as a function of the model parameters, yet provides…