arXiv subjects

Oleg Chernoyarov

Publications and source records attributed to Oleg Chernoyarov.

3 recordsLinked to original sources

arXiv2018

Model selection for the robust efficient signal processing observed with small Lévy noise

We develop a new model selection method for the adaptive robust efficient nonparametric signal estimation observed with impulse noise which is defined by the general non Gaussian Lévy processes. On the basis of the developed method, we construct the estimation procedures which are analyzed in two settings: in non asymptotic and asymptotic ones. For the first time for such models we show non asymptotic sharp oracle inequalities for the quadratic and for the robust risks, i.e. we show that the constructed procedures are optimal in the sharp oracle inequalities sense. Next, by making use of the obtained oracle inequalities, we provide the asymptotic efficiency property for the developed estimation methods in the adaptive setting when the signal/noise ratio goes to infinity. We apply the developed model selection methods for the signals number detection problem in multi-path information transmission.

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arXiv2015

On Misspecifications in Regularity and Properties of Estimators

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.

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arXiv2015

On Parameter Estimation for Cusp-type Signals

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.

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