A Fuzzy Approach for Randomized Confidence Intervals

TL;DR

This paper introduces a fuzzy approach to construct randomized confidence intervals that are more adaptable to irregular distributions, outperforming traditional methods especially in high-variance scenarios.

Contribution

It presents a novel fuzzy confidence interval method based on Neyman-Pearson lemma, applicable to a wider range of distributions and achieving minimal maximum expected length.

Findings

Better performance in high-variance situations

Provides a lower bound for expected length

Achieves minimal maximum expected length for Bernoulli trials

Abstract

We propose randomized confidence intervals based on the Neyman-Pearson lemma, in order to make them more broadly applicable to distributions that do not satisfy regularity conditions. This is achieved by using the definition of fuzzy confidence intervals. These intervals are compared with methods described in the literature for well-known distributions such as normal, binomial, and Poisson. The results show that in high-variance situations, the new intervals provide better performance. Furthermore, through these intervals, it is possible to compute a lower bound for the expected length, demonstrating that they achieve the minimal maximum expected length for a Bernoulli trial observation.