Linear Response Estimators for Singular Statistical Models
Provides a theoretical foundation for sensitivity analysis in singular statistical models, which is important for model interpretation and robustness.
The paper defines susceptibilities to measure how observables in parameterized statistical models respond to data perturbations, and introduces estimators that are proven to be consistent and asymptotically unbiased for large sample sizes.
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.