基于最小复杂度准则的渐近最优函数估计

Proceedings of 1994 IEEE International Symposium on Information Theory Pub Date : 1994-12-01 DOI:10.1109/ISIT.1994.394933

A. Barron, Yuhong Yang, Bin Yu

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引用次数: 27

摘要

应用于函数估计的最小描述长度原则可以产生log(likelihood)+const/spl middot/m形式的标准，而不是熟悉的log(likelihood)+(m/2) log n，其中m是参数的数量，n是样本量。改进的准则对冗余和统计风险产生最小、最大的最优率。分析表明，Rissanen(1983)、Schwarz(1978)和Akaike(1973)提出的标准在信息论上是一致的。

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Asymptotically optimal function estimation by minimum complexity criteria

The minimum description length principle applied to function estimation can yield a criterion of the form log(likelihood)+const/spl middot/m instead of the familiar log(likelihood)+(m/2) log n where m is the number of parameters and n is the sample size. The improved criterion yields minimax optimal rates for redundancy and statistical risk. The analysis suggests an information-theoretic reconciliation of criteria proposed by Rissanen (1983), Schwarz (1978), and Akaike (1973).<>

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Proceedings of 1994 IEEE International Symposium on Information Theory

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