A new and flexible class of sharp asymptotic time-uniform confidence sequences

TL;DR

This paper introduces a new flexible class of sharp asymptotic confidence sequences that are time-uniform and robust, with connections to sequential testing, enhancing the reliability of statistical inference over time.

Contribution

It proposes a novel class of confidence sequences that achieve sharp asymptotic coverage under mild assumptions, improving robustness and flexibility in sequential analysis.

Findings

Provides a new limit theorem for the proposed confidence sequences.

Establishes the connection between confidence sequences and sequential testing.

Demonstrates the asymptotic optimality of the new confidence sequences.

Abstract

Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences are a nonparametric tool showing under which high-level assumptions asymptotic coverage is achieved so that they also give a certain robustness guarantee against distributional deviations. In this paper, we propose a new flexible class of confidence sequences yielding sharp asymptotic time-uniform confidence sequences under mild assumptions. Furthermore, we highlight the connection to corresponding sequential testing problems and detail the underlying limit theorem.