Related papers: Confidence intervals for intentionally biased esti…
Regulatory guidance notes the need for caution in the interpretation of confidence intervals (CIs) constructed during and after an adaptive clinical trial. Conventional CIs of the treatment effects are prone to undercoverage (as well as…
The recent paper "Simple confidence intervals for MCMC without CLTs" by J.S. Rosenthal, showed the derivation of a simple MCMC confidence interval using only Chebyshev's inequality, not CLT. That result required certain assumptions about…
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…
The purpose of the present paper is to assess the efficacy of confidence intervals for Rosenthal's fail-safe number. Although Rosenthal's estimator is highly used by researchers, its statistical properties are largely unexplored. First of…
Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this…
Cross-validation (CV) is one of the most widely used techniques in statistical learning for estimating the test error of a model, but its behavior is not yet fully understood. It has been shown that standard confidence intervals for test…
Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are…
The problem is in the estimation of the fraction of population with a sensitive characteristic. We consider the Item Count Technique an indirect method of questioning designed to protect respondents' privacy. The exact confidence interval…
Statistical analyses of multipopulation studies often use the data to select a particular population as the target of inference. For example, a confidence interval may be constructed for a population only in the event that its sample mean…
Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…
In empirical research, when we have multiple estimators for the same parameter of interest, a central question arises: how do we combine unbiased but less precise estimators with biased but more precise ones to improve the inference? Under…
Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this paper, we assess the performance of four common proportion interval estimators: the Wald,…
We study properties of confidence intervals (CIs) for the difference of two Bernoulli distributions' success parameters, $p_x - p_y$, in the case where the goal is to obtain a CI of a given half-width while minimizing sampling costs when…
Because of the constraint that the estimators be bona fide physical states, any quantum state tomography scheme - including the widely used maximum likelihood estimation - yields estimators that may have a bias, although they are consistent…
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…
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…
This paper studies inference for quadratic forms of linear regression coefficients with clustered data and many covariates. Our framework covers three important special cases: instrumental variables regression with many instruments and…
We consider the problem of constructing confidence intervals (CIs) for the population mean of $N$ values $\{x_1, \ldots, x_N\} \subset \Sigma^N$ based on a random sample of size $n$, denoted by $X^n \equiv (X_1, \ldots, X_n)$, drawn…
Classical frequentist approaches to inference for the lasso emphasize exact coverage for each feature, which requires debiasing and severs the connection between confidence intervals and the original lasso estimates. To address this, in…
Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a…