Linear Response Estimators for Singular Statistical Models

2026-05-08

AI Summary

This study addresses the lack of effective methods for quantifying how observables in singular statistical models respond to data perturbations. It introduces susceptibility as a central measure of this response and proposes, for the first time, an estimator for generalized observables grounded in linear response theory. By integrating statistical inference with asymptotic analysis, the estimator is shown to be consistent and asymptotically unbiased in the large-sample limit, relying solely on $n$ observed data points. This work establishes the first theoretically guaranteed framework for sensitivity analysis in singular statistical models, providing rigorous foundations for assessing the stability of model outputs under infinitesimal data perturbations.

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.

Problem

• Linear Response
• Singular Statistical Models
• Susceptibility
• Estimators
• Asymptotic Unbiasedness

Innovation

• Linear Response
• Singular Statistical Models
• Susceptibility Estimators
• Consistency
• Asymptotic Unbiasedness