Credible intervals and bootstrap confidence intervals in monotone regression

TL;DR

This paper reinterprets a Bayesian credible interval method for monotone regression as a bootstrap approach, demonstrating the advantages of a smoothed bootstrap over percentile methods through theoretical proofs.

Contribution

It provides a frequentist perspective on a Bayesian method, introduces two bootstrap versions, and shows the superiority of a smoothed bootstrap in monotone regression.

Findings

Smoothed bootstrap has better coverage properties.

Percentile bootstrap requires correction for coverage.

Martingale methods underpin the proofs.

Abstract

In the recent paper [5], a Bayesian approach for constructing confidence intervals in monotone regression problems is proposed, based on credible intervals. We view this method from a frequentist point of view, and show that it corresponds to a percentile bootstrap method of which we give two versions. It is shown that a (non-percentile) smoothed bootstrap method has better behavior and does not need correction for over- or undercoverage. The proofs use martingale methods.