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Nonparametric hypothesis testing with small type I or type II error probabilities

Abstract

For the problem of signal detection in Gaussian white noise, we obtain lower bounds for the asymptotics of moderate deviation probabilities of type I and type II errors. These asymptotics are attained on tests of the χ 2 type. Using these lower bounds, we find lower bounds for nonparametric confidence estimation in the moderate deviation zone.

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Correspondence to M. S. Ermakov.

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Original Russian Text © M.S. Ermakov, 2008, published in Problemy Peredachi Informatsii, 2008, Vol. 44, No. 2, pp. 54–74.

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Ermakov, M.S. Nonparametric hypothesis testing with small type I or type II error probabilities. Probl Inf Transm 44, 119–137 (2008). https://doi.org/10.1134/S0032946008020051

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Keywords

  • Error Probability
  • Information Transmission
  • Moderate Deviation
  • Nonparametric Estimation
  • Nonparametric Estimator