Accuracy of approximation of Bayes estimates in presence of noninformative parameters

The asymptotic behavior of multidimensional a posterior distributions as the signal-to-noise ratio increases is used for construction of quasioptimum estimates. It is found that a maximum-likelihood estimate approximates a Bayes estimates with asymptotically decreasing mean square error. The procedure is applicable to a signal with a multidimensional Gaussian distribution of unknown parameters, calculation of the approximation error becoming quite simple when all unknown parameters are not energy related. A pulse signal with linear frequency modulation mixed with a white noise at the receiver input illustrates how the presence of a noninformative parameter, in this case the Gaussian random frequency, decreases the accuracy of this approximation for estimating the Gaussian random position of the signal in time.