We consider the problem of parameter estimation by the observations of deterministic signal in white gaussian noise. It is supposed that the signal has a singularity of cusp-type. The properties of the maximum likelihood and bayesian estimators are described in the asymptotics of small noise. Special attention is paid to the problem of parameter estimation in the situation of misspecification in regularity, i.e.; the statistician supposes that the observed signal has this singularity, but the real signal is smooth. The rate and the asymptotic distribution of the maximum likelihood estimator in this situation are described.MSC 2000 Classification: 62M02, 62G10, 62G20.
We considered a method for the determining of the statistical characteristics of the magnitude, location and first-passage time of Markov random process, with piecewise constant drift and diffusion coefficients. We found the closed analytical expressions for distribution functions of the specified random variables. We also analyzed the asymptotic behavior of probability density and ordinary moments of location of the greatest maximum of Markov random process and showed their coincidence with some known results for the particular cases.
We suggest a basic fast algorithm for the noncoherent digital processing of the radio signals consisting of the minimum number of simple arithmetic operations over a signal period. On its basis there can be realized the algorithms and the correspondent digital devices for detection and noncoherent demodulation of signals with amplitude, frequency modulation and differential phase keying. Digital signal processors and modern programmable logic devices can be effectively used for their practical implementation.
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