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We consider problem of signal detection in Gaussian white noise. Teststatistics are linear combinations of squares of estimators of Fouriercoefficients or $\mathbb{L}_2$-norms of kernel estimators. We point outnecessary and sufficient conditions when nonparametric sets of alternativeshave a given rate of exponential decay for type II error probabilities.

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