An asymptotic property of model selection criteria
Yuhong Yang
Barron, A.R.
Dept. of Stat., Iowa State Univ., Ames, IA;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Jan 1998
Volume: 44,
Issue: 1
On page(s): 95-116
ISSN: 0018-9448
References Cited: 48
CODEN: IETTAW
INSPEC Accession Number: 5812007
Digital Object Identifier: 10.1109/18.650993
Current Version Published: 2002-08-06
Abstract
Probability models are estimated by use of penalized
log-likelihood criteria related to Akaike (1973) information criterion
(AIC) and minimum description length (MDL). The accuracies of the
density estimators are shown to be related to the tradeoff between three
terms: the accuracy of approximation, the model dimension, and the
descriptive complexity of the model classes. The asymptotic risk is
determined under conditions on the penalty term, and is shown to be
minimax optimal for some cases. As an application, we show that the
optimal rate of convergence is simultaneously achieved for log-densities
in Sobolev spaces W2s(U) without knowing the
smoothness parameter s and norm parameter U in advance. Applications to
neural network models and sparse density function estimation are also
provided
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