An asymptotic property of model selection criteria
An asymptotic property of model selection criteria
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DOI：
10.1109/18.650993
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发表时间：
1998-01-01
影响因子：
2.5
通讯作者：
Barron, AR
中科院分区：
文献类型：
--
作者：
Yang, YH;Barron, AR
利用与AIC和MDL相关的惩罚对数似然准则对概率模型进行估计，证明了密度估计的精度与逼近精度、模型维度和模型类的描述复杂性之间的权衡有关，在惩罚项的条件下确定了渐近风险，并且在某些情况下证明了渐近风险是极小极大最优的。作为应用，我们证明了在不预先知道光滑参数S和范数参数U的情况下，对数密度在Sobolev空间W-2(S)(U)中同时达到了最优收敛速度，并给出了在神经网络模型和稀疏密度函数估计中的应用。
Probability models are estimated by use of penalized log-likelihood criteria related to AIC and 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 W-2(s)(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.