Le cam theory on the comparison of statistical models

Abstract

We recall the main concepts of the Le Cam theory of statistical experiments , especially the notion of Le Cam distance and its properties. We also review classical tools for bounding such a distance before presenting some examples. A proof of the classical equivalence result between density estimation problems and Gaussian white noise models will be analyzed.

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• Asymptotic comparison of negative multinomial and multivariate normal experiments
• Asymptotic efficiency for covariance estimation under noise and asynchronicity