Chapter 5 Distances between statistical models
نویسنده
چکیده
SECTION 1 explains why randomizations in the Le Cam sense have advantages over Markov kernels for the definition of the Le Cam distance between statistical models. SECTION 2 derives several facts about linear functionals, the most important being the existence of a linear map that projects onto the space of countably additive measures. SECTION 3 uses the projection map from Section 2, and compactness results for the space of generalized randomizations, to establish the assertions from Section 1. SECTION 4 establishes a coupling bound for the Le Cam distance between two statistical models. SECTION 5 defines local asymptotic normality (LAN). SECTION 6 interprets of δ(P,Q) via risk functions.
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