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Article Dans Une Revue Bernoulli Année : 2019

Probability measure characterization by L^p-quantization error function

Résumé

We establish conditions to characterize probability measures by their L^p-quantization error functions in both R^d and Hilbert settings. This characterization is two-fold: static (identity of two distributions) and dynamic (convergence for the L^p-Wasserstein distance). We first propose a criterion on the quantization level N, valid for any norm on Rd and any order p based on a geometrical approach involving the Voronoi diagram. Then, we prove that in the L^2-case on a (separable) Hilbert space, the condition on the level N can be reduced to N = 2, which is optimal. More quantization based characterization cases in dimension 1 and a discussion of the completeness of a distance defined by the quantization error function can be found at the end of this paper.
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Dates et versions

hal-02406592 , version 1 (12-12-2019)

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Yating Liu, Gilles Pagès. Probability measure characterization by L^p-quantization error function. Bernoulli, In press, 26 (2), ⟨10.3150/19-BEJ1146⟩. ⟨hal-02406592⟩
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