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Zapiski Nauchnykh Seminarov POMI, 2022, Volume 510, Pages 124–142
(Mi znsl7197)
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Nonparametric signal detection with small values of type I and type II error probabilities
M. S. Ermakovab a Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg
b St. Petersburg State University, Mathematics and Mechanics Faculty
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.
Key words and phrases:
goodness of fit tests, consistency, signal detection, Bickel–Rosenblatt test, Neyman test, maxisets.
Received: 04.07.2022
Citation:
M. S. Ermakov, “Nonparametric signal detection with small values of type I and type II error probabilities”, Probability and statistics. Part 32, Zap. Nauchn. Sem. POMI, 510, POMI, St. Petersburg, 2022, 124–142
Linking options:
https://www.mathnet.ru/eng/znsl7197 https://www.mathnet.ru/eng/znsl/v510/p124
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Statistics & downloads: |
Abstract page: | 46 | Full-text PDF : | 23 | References: | 12 |
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