Related papers: A New Confidence Interval for Odds Ratio

Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…

We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially…

In this article, we consider the problem of constructing the confidence interval and testing hypothesis for the common coefficient of variation (CV) of several normal populations. A new method is suggested using the concepts of generalized…

In this paper, we derive an explicit formula for constructing the confidence interval of binomial parameter with guaranteed coverage probability. The formula overcomes the limitation of normal approximation which is asymptotic in nature and…

A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…

Suppose the lifetime of a large sample of batteries in routine use is measured. A confidence interval is computed to 394 plus/minus 1.96 times 4.6 days. The standard interpretation is that if we repeatedly draw samples and compute…

Turing's estimator allows one to estimate the probabilities of outcomes that either do not appear or only rarely appear in a given random sample. We perform a simulation study to understand the finite sample performance of several related…

In this paper, we develop an exact method for computing the minimum coverage probability of Wald interval for estimation of binomial parameters. Similar approach can be used for other type of confidence intervals.

We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large…

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…

Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…

We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a…

For any class of one-sided $1-\alpha$ confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two…

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…

Small sample sizes in clinical studies arises from factors such as reduced costs, limited subject availability, and the rarity of studied conditions. This creates challenges for accurately calculating confidence intervals (CIs) using the…

Several scientific fields including psychology are undergoing a replication crisis. There are many reasons for this problem, one of which is a misuse of p-values. There are several alternatives to p-values, and in this paper we describe a…

We derive a computationally convenient formula for the large sample coverage probability of a confidence interval for a scalar parameter of interest following a preliminary hypothesis test that a specified vector parameter takes a given…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…

This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of…