Anytime valid and asymptotically optimal inference driven by predictive recursion

TL;DR

This paper introduces a new e-process based on predictive recursion that provides anytime valid and asymptotically optimal inference for model discrimination, especially useful in complex nonparametric settings without known stopping rules.

Contribution

It develops a novel e-process using predictive recursion, enabling valid sequential testing and asymptotic efficiency in nonparametric model comparison.

Findings

Provides anytime valid inference in complex models

Achieves first-order asymptotic optimality

Applicable without known stopping rules

Abstract

Distinguishing two candidate models is a fundamental and practically important statistical problem. Error rate control is crucial to the testing logic but, in complex nonparametric settings, can be difficult to achieve, especially when the stopping rule that determines the data collection process is not available. This paper proposes an e-process construction based on the predictive recursion (PR) algorithm originally designed to recursively fit nonparametric mixture models. The resulting PRe-process affords anytime valid inference and is asymptotically efficient in the sense that its growth rate is first-order optimal relative to PR's mixture model.