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

2022/06/29 by Ermakov, Mikhail
#62F03 #62G10 #62G2 #FOS: Mathematics #G.3 #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2206.14511

Abstract

We consider problem of signal detection in Gaussian white noise. Test statistics are linear combinations of squares of estimators of Fourier coefficients or \mathbbL₂-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.

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