No abstract

The problem of parameter estimation by the continuous time observations of a deterministic signal in white gaussian noise is considered. The asymptotic properties of the maximul likelihood estimator are described in the asymptotics of small noise (large siglal-to-noise ratio). We are interested by the situation when there is a misspecification in the regularity conditions. In particular it is supposed that the statistician uses a discontinuous (change-point type) model of signal, when the true signal is continuously differentiable function of the unknown parameter.MSC 2000 Classification: 62M02, 62G10, 62G20.

We are considering a problem of the measurement of the dispersion of the random pulse signal with unknown time of arrival against the white noise and the correlated Gaussian interference. By applying a maximum likelihood method, we synthesize quasi-optimal, quasi-likelihood and adaptive estimation algorithms. We also find out the theoretical and experimental dependences for the characteristics of the obtained dispersion estimates that are then used in the study of the efficiency of the introduced algorithms and in the further investigation revea-6936 O.V. Chernoyarov et al. ling the loss in estimation accuracy, due to the absence of the prior information on intensity of operational interferences. We are to show that, with the adaptation in terms of intensity of the correlated interference, it is possible to obtain the dispersion estimate independent from the intensity of white noise, and its characteristics coincide asymptotically with the corresponding characteristics of the dispersion estimate, obtained under the a priori known intensities of interference and white noise.

No abstract

No abstract