Asymptotically Optimal Sequential Estimation of the Mean Based on Inclusion Principle

TL;DR

This paper introduces a sequential estimation method for the mean that guarantees coverage probabilities using confidence sequences, with proven asymptotic optimality for a broad class of problems.

Contribution

It presents a general approach for constructing random intervals for the mean using the inclusion principle, providing asymptotic optimality results.

Findings

Method guarantees pre-specified coverage probabilities.

Asymptotic optimality of the sequential estimation approach.

Applicable to a wide range of scientific and engineering problems.

Abstract

A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference of mean values based on accumulated observational data. We show that the construction of such random intervals can be accomplished by comparing the endpoints of random intervals with confidence sequences for the mean. Asymptotic results are obtained for such sequential methods.