Nonparametric signal detection with small values of type I and type II error probabilities

TL;DR

This paper investigates nonparametric signal detection in Gaussian noise, establishing conditions for exponential decay rates of type II error probabilities using specific test statistics.

Contribution

It provides necessary and sufficient conditions for the exponential decay of type II errors in nonparametric signal detection with small error probabilities.

Findings

Identifies conditions for exponential decay of type II errors.

Analyzes linear combinations of Fourier coefficient squares.

Focuses on Gaussian white noise signal detection.

Abstract

We consider problem of signal detection in Gaussian white noise. Test statistics are linear combinations of squares of estimators of Fourier coefficients or $\mathbb{L}_2$-norms of kernel estimators. We point out necessary and sufficient conditions when nonparametric sets of alternatives have a given rate of exponential decay for type II error probabilities.