On asymptotically efficient statistical inference on a signal parameter

TL;DR

This paper investigates the fundamental limits of statistical inference for signal parameters in Gaussian noise, establishing lower bounds on efficiency for confidence estimation and hypothesis testing in moderate deviation regimes.

Contribution

It derives new asymptotic efficiency bounds for signal parameter inference in Gaussian noise, extending classical minimax and Pitman efficiency bounds to moderate deviation probabilities.

Findings

Established lower bounds for confidence estimation in Gaussian noise

Derived asymptotic efficiency bounds for hypothesis testing

Extended classical bounds to moderate deviation regimes

Abstract

We consider the problems of confidence estimation and hypothesis testing on a parameter of signal observed in Gaussian white noise. For these problems we point out lower bounds of asymptotic efficiency in the zone of moderate deviation probabilities. These lower bounds are versions of local asymptotic minimax Hajek-Le Cam lower bound in estimation and the lower bound for Pitman efficiency in hypothesis testing. The lower bounds were obtained for both logarithmic and sharp asymptotic of moderate deviation probabilities.