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Gaussian model selection

Lucien Birgé, Pascal Massart (2001)

Journal of the European Mathematical Society

Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models,...

Generalized covariance inequalities

Przemysław Matuła, Maciej Ziemba (2011)

Open Mathematics

We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.

Generalized regression estimation for continuous time processes with values in functional spaces

Bertrand Maillot, Christophe Chesneau (2021)

Commentationes Mathematicae Universitatis Carolinae

We consider two continuous time processes; the first one is valued in a semi-metric space, while the second one is real-valued. In some sense, we extend the results of F. Ferraty and P. Vieu in ``Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination'' (2004), by establishing the convergence, with rates, of the generalized regression function when a real-valued continuous time response is considered. As corollaries, we deduce the...

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