Optimal algorithms of data processing for complex information and telecommunication systems in an uncertain environment

Abstract : This thesis is devoted to the problem of non parametric estimation for continuous-time regression models. We consider the problem of estimating an unknown periodoc function S. This estimation is based on observations generated by a stochastic process; these observations may be in continuous or discrete time. To this end, we construct a series of estimators by projection and thus we approximate the unknown function S by a finite Fourier series. In this thesis we consider the estimation problem in the adaptive setting, i.e. in situation when the regularity of the fonction S is unknown. In this way, we develop a new adaptive method based on the model selection procedure proposed by Konev and Pergamenshchikov (2012). Firstly, this procedure give us a family of estimators, then we choose the best possible one by minimizing a cost function. We give also an oracle inequality for the risk of our estimators and we give the minimax convergence rate.
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Slim Beltaief. Optimal algorithms of data processing for complex information and telecommunication systems in an uncertain environment. Numerical Analysis [math.NA]. Normandie Université, 2017. English. ⟨NNT : 2017NORMR056⟩. ⟨tel-01692095⟩

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