Cross-validation method for bivariate measure with certain mixture

International audienceWe consider a pair of random variables (X; Y ) whose probability measure is thesum of an absolutely continuous measure, a discrete measure and a finite number of absolutelycontinuous measures on several lines. An asymptotically unbiased and consistent estimate ofthe density of the continuous part is given in [13]. In this work, we focus on the choice of theseparameters so that this estimate will be optimal and the rate of convergence will be better. weas well as its rate of convergence. To achieve this we use the cross-validation technics

Discrete estimation of spectral density for symmetric stable process

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Estimation of the constant measurement error of stable random field

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Ecrits sur les processus aléatoires, Analyse spectrale des processus alpha stables

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The Choice of the Smoothing Parameter for Alpha Stable Signals

International audienceIn this work we consider the class of symmetricalpha stable processes which are a particular family ofprocesses with infinite energy. These processes used inmodeling the random signals with indefinitely growingvariance. The spectral density estimator of such signals isgiven in the literature by smoothing the periodogram by aspectral window. Thus, the estimator depends on the widthof the spectral window considered as a smoothing parameter.The choice of this parameter plays an important role sincethe rate of convergence of the estimator is a function of thisparameter. The objective of this paper is to propose amethod giving the optimal parameter based on the crossvalidation technique (minimization of MISE: MeanIntegrate Square of Error). We establish a criterionfunction and we prove that the mean of this criterionconverges to MISE. Thus, we show that the valueminimizing this criterion is the optimal smoothingparameter. The rate of convergence of the estimator hasbeen studied in order to prove that the smoothingparameter obtained by this method gives the fastestconvergence of the estimator towards the spectral density

Spectral density estimate for alpha-stable p-adic processes

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Spectral Density Estimate for Stable Processes Observed with an Additive Error

International audienceIn this paper, a symmetric alpha stable process where its spectral representation has an additive error is considered. The error is supposed to be constant. A periodogram as estimator of the spectral density and its rate of convergence are given. In order to give an asymptotically unbiased and consistent estimate of the spectral density, this periodogram is smoothed by an adapted spectral window. The rate of convergence is given

Spectral density estimation for stationary stable random fields.

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Nonparametric density estimation of continuous part of a mixed measure

We consider a pair of random variables(X,Y) whose probability measure is the sum of an absolutely continuous measure, a discrete measure and a finite number of absolutely continuous measures on several lines(1). An asymptotically unbiased and consistent estimate, at all points, of the density of the continuous part is given as well as its rate of convergence. We also estimate the amplitude of the discrete measure and the densities on several lines

Estimation de la densité de la mesure spectrale mixte pour un processus symétrique stable strictement stationnaire

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