Slim Beltaief | Searcharxiv

arXiv2020

Robust adaptive efficient estimation for a semi-Markov continuous time regression from discrete data

In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp non-asymptotic oracle inequality for the robust risks is obtained. We obtain sufficient conditions on the frequency observations under which the robust efficiency is shown. It turns out that for the semi-Markov models the robust minimax convergence rate may be faster or slower than the classical one.

math.ST↗

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.

math.ST↗