Related papers: Higher-order approximate confidence intervals
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
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…
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…
Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes,…
Practical or scientific considerations often lead to selecting a subset of parameters as ``important.'' Inferences about those parameters often are based on the same data used to select them in the first place. That can make the reported…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
We consider the problem of setting confidence intervals on a parameter of interest from the maximum-likelihood fit of a physics model to a binned data set with a large number of bins, large event-counts per bin, and in the presence of…
Confidence interval of mean is often used when quoting statistics. The same rigor is often missing when quoting percentiles and tolerance or percentile intervals. This article derives the expression for confidence in percentiles of a sample…
Recent advances in quasi-Monte Carlo integration have shown that for linearly scrambled digital net estimators, the convergence rate can be dramatically improved by taking the median rather than the mean of multiple independent replicates.…
Conformal prediction provides prediction sets with coverage guarantees. The informativeness of conformal prediction depends on its efficiency, typically quantified by the expected size of the prediction set. Prior work on the efficiency of…
Under standard regularity assumptions, we provide simple approximations for specific classes of fiducial and confidence distributions and discuss their connections with objective Bayesian posteriors. For a real parameter the approximations…
I propose a new type of confidence interval for correct asymptotic inference after using data to select a model of interest without assuming any model is correctly specified. This hybrid confidence interval is constructed by combining…
We provide analytic formulas for the standard error and confidence intervals for the F measures, based on a property of asymptotic normality in the large sample limit. The formula can be applied for sample size planning in order to achieve…
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…
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…
In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of…
The current standard for confidence interval construction in the context of a possibly misspecified model is to use an interval based on the sandwich estimate of variance. These intervals provide asymptotically correct coverage, but…
We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…
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…