Abstract:
The author investigates the asymptotic properties of maximum-likelihood estimates and Bayesian estimates of a univariate parameter when a continuous signal is transmitted over a channel with arbitrary Gaussian noise. In terms of the norms of a signal and its derivative with respect to a parameter in Hilbert space, for which the correlation function of the noise acts as a reproducing kernel, conditions are found that guarantee that these estimates will be asymptotically normal, consistent, and asymptotically effective. Transmission of a harmonic signal over a channel with stationary noise is considered as an example.
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