Rolando Biscay (CIMAT-CONACYT)
Estimation of covariance functions as a model selection problem.
We review several results of collaborative work with researchers from the University of Toulouse (France) about estimation of covariance functions by model selection. They are based on stating the problem of covariance function estimation as a matrix-valued linear regression problem through expansion on a basis functions. Concentration inequalities are extended from the univariate linear regression model to this new setting, which allows to elaborate a consistent model selection strategy for covariance function estimation with bounds on its risk for finite samples. Furthermore, the introduced estimate fulfills the key requirement of being a nonnegative definitive function.
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