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Sharp oracle inequalities and slope heuristic for specification probabilities estimation in general random fields

13 June 2011
M. Lerasle
D. Takahashi
ArXiv (abs)PDFHTML
Abstract

We provide new methods for estimation of the one-point specification probabilities in general discrete random fields. Our procedures are based on model selection by minimization of a penalized empirical criterion. The selected estimators satisfy sharp oracle inequalities without any assumption on the random field for both L2L_{2}L2​-risk and K\"ullback loss. We also prove the validity of slope heuristic for the specification probabilities estimation problem. We finally show in simulation studies the practical performances of our methods.

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