Sequential Estimation Methods from Inclusion Principle

TL;DR

This paper introduces new sequential estimation methods that utilize the inclusion principle to construct confidence sequences, providing rigorous guarantees on coverage probabilities unlike traditional asymptotic approaches.

Contribution

It presents a novel framework for sequential estimation based on the inclusion principle, ensuring exact confidence levels in finite samples.

Findings

Guarantees exact coverage probabilities for sequential estimates.

Provides a new formulation of estimation problems as constructing sequential random intervals.

Improves reliability of sequential estimation methods.

Abstract

In this paper, we propose new sequential estimation methods based on inclusion principle. The main idea is to reformulate the estimation problems as constructing sequential random intervals and use confidence sequences to control the associated coverage probabilities. In contrast to existing asymptotic sequential methods, our estimation procedures rigorously guarantee the pre-specified levels of confidence.