Linear Response Estimators for Singular Statistical Models

TL;DR

This paper introduces susceptibility measures for statistical models, proposing estimators that are consistent and asymptotically unbiased as data size grows.

Contribution

It defines a new class of susceptibility estimators for parameterized models and proves their statistical properties.

Findings

Estimators are consistent with large data samples.

Estimators are asymptotically unbiased.

Applicable to a broad class of observables.

Abstract

We define susceptibilities as a measure of the response of an observable quantity of a parameterized statistical model to a perturbation of the data for a general class of observables. We define estimators for these susceptibilities as statistics in a sequence of n data-points and prove that these estimators are consistent and asymptotically unbiased in the large n regime.