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On rates of convergence of efficient detection criteria in signal processing with white noise. (English) Zbl 0677.94001
In this paper one established the strong consistency and the rate of convergence of Efficient Detection Criteria (EDC). The EDC for cases where the noise variance is either known or unknown and the underlying distribution is not necessarly normal is also presented. One states the problems which arises in the area of signal processing. The upper bounds of the wrong detection probability by means of the special structure of the sample covariance matrix are obtained. The results of the simulations for different eigenvalues $\lambda$ (2,3,5) of the covariance matrix with dimension $p=10$ and signal member $q=5$ are discussed. For this eigenvalues the SNR is equal to 0,3 and 6 dB respectively. By using the exponential function exp(a-bC(N)) where a and b are constants and C(N) is the threshold for a fixed sample size N, the curves of frequency of error detections are given. The sample size runs from 30 to 1000, with 1000 repetitions. Many particulary cases and remarks for differents values of C(N), N, a and b are described.
Reviewer: P.Cotae

MSC:
94A12Signal theory (characterization, reconstruction, filtering, etc.)
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