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The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level…

Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…

When comparing the citation impact of nations, departments or other groups of researchers within individual fields, three approaches have been proposed: arithmetic means, geometric means, and percentage in the top X%. This article compares…

We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices…

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…

By employing various empirical estimators for the Mutual Information (MI) measure, we calculate and compare the estimates and their confidence intervals for both normal and non-normal bivariate data samples. We find that certain nonlinear…

Computation of confidence sets is central to data science and machine learning, serving as the workhorse of A/B testing and underpinning the operation and analysis of reinforcement learning algorithms. This paper studies the geometry of the…

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…

We propose a method for estimating disparity confidence intervals in stereo matching problems. Confidence intervals provide complementary information to usual confidence measures. To the best of our knowledge, this is the first method…

I present a critical review of techniques for estimating confidence intervals on binomial population proportions inferred from success counts in small-to-intermediate samples. Population proportions arise frequently as quantities of…

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…

We present methodology for constructing pointwise confidence intervals for the cumulative distribution function and the quantiles of mixing distributions on the unit interval from binomial mixture distribution samples. No assumptions are…

Inequalities may appear in many models. They can be as simple as assuming a parameter is nonnegative, possibly a regression coefficient or a treatment effect. This paper focuses on the case that there is only one inequality and proposes a…

When computing a confidence interval for a binomial proportion p one must choose between using an exact interval, which has a coverage probability of at least 1-{\alpha} for all values of p, and a shorter approximate interval, which may…

We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…

We provide adaptive confidence intervals on a parameter of interest in the presence of nuisance parameters when some of the nuisance parameters have known signs. The confidence intervals are adaptive in the sense that they tend to be short…

The age of big data has produced data sets that are computationally expensive to analyze and store. Algorithmic leveraging proposes that we sample observations from the original data set to generate a representative data set and then…

In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…

Randomization-based inference commonly relies on grid search methods to construct confidence intervals by inverting hypothesis tests over a range of parameter values. While straightforward, this approach is computationally intensive and can…

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…