Adaptive model selection
Adaptive model selection
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DOI：
10.1198/016214502753479356
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发表时间：
2002-03-01
影响因子：
3.7
通讯作者：
Ye, JM
中科院分区：
文献类型：
--
作者：
Shen, XT;Ye, JM
大多数模型选择程序使用固定的罚款来惩罚模型大小的增加。这些非适应性选择过程只在一种情况下表现良好。例如，贝叶斯信息准则（BIC）与一个大的惩罚表现良好的“小”模型和“大”模型差，和赤池的信息准则（AIC）正好相反。本文提出了一种自适应模型选择过程，它使用基于广义自由度概念的数据自适应复杂度惩罚。建议的程序，结合一类非自适应程序的好处，近似的最佳性能，这类程序在各种不同的情况下。这一类别包括许多众所周知的程序，如AIC、BIC、Mallow's C-p和风险膨胀准则（RIC）。所提出的方法适用于非参数回归中的小波阈值和最小二乘回归中的变量选择。仿真结果和渐近分析支持所提出的方法的有效性。
Most model selection procedures use a fixed penalty penalizing an increase in the size of a model. These nonadaptive selection procedures perform well only in one type of situation. For instance, Bayesian information criterion (BIC) with a large penalty per-forms well for "small" models and poorly for "large" models, and Akaike's information criterion (AIC) does just the opposite. This article proposes an adaptive model selection procedure that uses a data-adaptive complexity penalty based on a concept of generalized degrees of freedom. The proposed procedure, combining the benefit of a class of nonadaptive procedures, approximates the best performance of this class of procedures across a variety of different situations. This class includes many well-known procedures, such as AIC, BIC, Mallows's C-p, and risk inflation criterion (RIC). The proposed procedure is applied to wavelet thresholding in nonparametric regression and variable selection in least squares regression. Simulation results and an asymptotic analysis support the effectiveness of the proposed procedure.