Contributions to predictive density estimation and Ridge estimator

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Adaptive Ridge estimation and Stein's effect under S-Hellinger distance and Density Power Divergence

This thesis focuses on the problem of statistical decision theory in two different contexts.

We consider the corresponding empirical mean for the Bayes estimator, as well as the predictive estimate of multivariate observable density; measured by the frequentist risk corresponding to two measures of divergence, namely: the divergence of density at power (Density Power Divergence), then under the family of distances S-Hellinger (SHD).

Both are considered a set of loss functions ($\alpha$ in [0,1]).

In the third chapter, we examine the effectiveness of estimators with predictive densities, multivariate observables measured by the frequentist risk corresponding to the SHD.Thus, the results established for the integrated squared error (ie the norm $L_2$ for $\alpha =1$), are extended to a larger frame.

Still in a framework of decision theory, the last and second part deals with the regression adaptive Ridge estimation, in a general linear model, with homogeneous errors with spherical symmetry.

A restriction on the regression parameter is considered, ie, under stress that all the regression coefficients are positive.

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