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Minimax detection of a signal in ℓp metrics

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Abstract

The problem of the minimax detection of a signal is considered in a Gaussian white noise of intensity ε → 0. The set of the signals represents an ellipsoid in the ℓp-metric with lengths of semiaxes ak −1 → 0 as k → ∞, from which a ball of radius ρε → 0 as ε → 0 in the ℓp-metric has been removed. Asymptotically minimax tests have been constructed for the cases 1 < p ≤ ∞ and asymptotically sharp estimates of the minimax efficiency have been obtained.

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Authors
  1. Yu. I. Ingster
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 152–168, 1990.

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Ingster, Y.I. Minimax detection of a signal in ℓp metrics. J Math Sci 68, 503–515 (1994). https://doi.org/10.1007/BF01254275

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  • DOI: https://doi.org/10.1007/BF01254275

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