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

06/29/2022

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by   Mikhail Ermakov, et al.

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