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October 2006 From ɛ-entropy to KL-entropy: Analysis of minimum information complexity density estimation
Tong Zhang
Ann. Statist. 34(5): 2180-2210 (October 2006). DOI: 10.1214/009053606000000704


We consider an extension of ɛ-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.


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Tong Zhang. "From ɛ-entropy to KL-entropy: Analysis of minimum information complexity density estimation." Ann. Statist. 34 (5) 2180 - 2210, October 2006.


Published: October 2006
First available in Project Euclid: 23 January 2007

zbMATH: 1106.62005
MathSciNet: MR2291497
Digital Object Identifier: 10.1214/009053606000000704

Primary: 62C10 , 62G07

Keywords: Bayesian posterior distribution , Density estimation , minimum description length

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 5 • October 2006
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