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From ε-Entropy to KL-Entropy: Analysis of Minimum Information Complexity Density Estimation

Zhang, Tong

The Annals of statistics, 2006-10, Vol.34 (5), p.2180-2210 [Periódico revisado por pares]

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Título:
From ε-Entropy to KL-Entropy: Analysis of Minimum Information Complexity Density Estimation
Autor: Zhang, Tong
Assuntos: Average linear density ; Bayes theorem ; Density ; Density estimation ; Determinism ; Entropy ; Estimation methods ; Estimators ; Exact sciences and technology ; Mathematics ; Nonparametric inference ; Nonparametric Statistical Analysis ; Perceptron convergence procedure ; Probability and statistics ; Random allocation ; Sciences and techniques of general use ; Statistics ; Sufficiency and information
É parte de: The Annals of statistics, 2006-10, Vol.34 (5), p.2180-2210
Descrição: We consider an extension of ε-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the statistical complexity of some deterministic and randomized density estimators. Consequences of the new inequality will be presented. In particular, we show that this technique can lead to improvements of some classical results concerning the convergence of minimum description length and Bayesian posterior distributions. Moreover, we are able to derive clean finite-sample convergence bounds that are not obtainable using previous approaches.
Editor: Hayward, CA: Institute of Mathematical Statistics
Idioma: Inglês

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