Multiscale inference about a density

TL;DR

This paper presents a multiscale statistical method for detecting and localizing increases or decreases in a density or failure rate, offering finite-sample guarantees and asymptotic optimality.

Contribution

It introduces a novel multiscale test statistic based on local order statistics and spacings, enabling simultaneous confidence statements with guaranteed significance levels.

Findings

Provides finite-sample significance guarantees

Achieves asymptotic optimality and adaptivity

Easy to implement in practical scenarios

Abstract

We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The procedure provides guaranteed finite-sample significance levels, is easy to implement and possesses certain asymptotic optimality and adaptivity properties.