Related papers: Confidence Limits and their Robustness
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
Computational method for statistical measures of reliability, confidence, and assurance are available for infinite population size. If the population size is finite and small compared to the number of samples tested, these computational…
The determination of the true source polarization given a set of measurements is complicated by the requirement that the polarization always be positive. This positive bias also hinders construction of upper limits, uncertainties, and…
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…
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…
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…
By combining a bound on the absolute value of the difference of mutual information between two joint probablity distributions with a fixed variational distance, and a bound on the probability of a maximal deviation in variational distance…
We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…
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…
We formalize the idea of probability distributions that lead to reliable predictions about some, but not all aspects of a domain. The resulting notion of `safety' provides a fresh perspective on foundational issues in statistics, providing…
We define some appropriate statistical quantities that indicate the physical significance (reliability) of confidence intervals in the framework of both Frequentist and Bayesian statistical theories. We consider the expectation value of the…
We present a procedure for handling asymmetric errors. Many results in particle physics are presented as values with different positive and negative errors, and there is no consistent procedure for handling them. We consider the difference…
We study the frequentist properties of confidence intervals for the On-Off problem. The methods include all those in common use today. We derive explicit formulas for the limits and calculate the true coverage and the expected lengths of…
Credibility theory provides tools to obtain better estimates by combining individual data with sample information. We apply the Credibility theory to a Uniform distribution that is used in testing the reliability of forecasting an interest…
This note points out how confidence interval estimates for standard deviation transform into confidence interval estimates for the power of F-tests at fixed alternative means. An application is shown for the test of a two-sided hypothesis…
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…
Prediction sets provide a means of quantifying the uncertainty in predictive tasks. Using held out calibration data, conformal prediction and risk control can produce prediction sets that exhibit statistically valid error control in a…
In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that…
A calculator program has been written to give confidence intervals on branching ratios for rare decay modes (or similar quantities) calculated from the number of events observed, the acceptance factor, the background estimate and the…
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…