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On Asymptotically Efficient Statistical Inference on a Signal Parameter

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We consider the problems of confidence estimation and hypotheses testing of the parameter of a signal observed in a Gaussian white noise. For these problems, we point out lower bounds of asymptotic efficiency in the zone of moderate deviation probabilities. These lower bounds are versions of the local asymptotic minimax Hajek–Le Cam lower bound in estimation and the lower bound for the Pitman efficiency in hypotheses testing. The lower bounds are obtained both for logarithmic and sharp asymptotics of moderate deviation probabilities.

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Authors and Affiliations

  1. Institute of Problems of Mechanical Engineering of RAS, St. Petersburg State University, St. Petersburg, Russia

    M. S. Ermakov

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  1. M. S. Ermakov
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Correspondence to M. S. Ermakov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 420, 2013, pp. 70–87.

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Ermakov, M.S. On Asymptotically Efficient Statistical Inference on a Signal Parameter. J Math Sci 206, 159–170 (2015). https://doi.org/10.1007/s10958-015-2300-1

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