Statistical Inference via T-Posterior Randomised Estimators

TL;DR

This paper introduces a new estimation method that produces randomized estimators for unknown distributions, with proven performance bounds and robustness, demonstrated through Poisson process intensity estimation.

Contribution

It presents a novel estimation approach that avoids traditional concentration inequalities, offering non-asymptotic bounds and robustness to model misspecification.

Findings

Establishes non-asymptotic performance bounds for the estimators.

Demonstrates robustness to potential model misspecification.

Provides an application to estimating Poisson process intensity.

Abstract

Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and demonstrate their robustness to potential model misspecification. Notably, these properties are established by circumventing the use of concentration inequalities and empirical process theory. We provide an illustration of this approach to the problem of estimating the intensity of a Poisson process.