Adaptive model selection and assessment for exponential family distributions
Adaptive model selection and assessment for exponential family distributions
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DOI：
10.1198/004017004000000338
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发表时间：
2004-08-01
期刊：
影响因子：
2.5
通讯作者：
Ye, J
中科院分区：
文献类型：
--
作者：
Shen, XT;Huang, HC;Ye, J
在许多科学和工程问题中，从大量的候选模型中选择最优模型是很重要的，特别是在数据挖掘中。在文献中，在非正态分布的背景下，模型评估尚未得到很多关注。事实上，许多现有的模型选择标准，如贝叶斯信息标准和C-p，可能不适合于条件均值和方差的响应是依赖的情况下，如在广义线性模型回归。在这篇文章中，我们提出了一个新的自适应模型选择准则，并构造了一个近似无偏的Kullback-Leibler损失估计模型评估的背景下，指数族分布。这允许比较任意复杂的建模过程。我们的建议使用了一个称为广义自由度的概念，它概括了最初为正态分布提出的概念。所提出的程序实现的二项分布和泊松分布和其小样本操作特性，通过模拟检查。空气污染对某些呼吸道疾病的影响的研究应用程序证明了该方法的实用性。数值分析支持该方法的实用性。
In many scientific and engineering problems, selecting the optimal model from a large pool of candidate models is important, particularly in data mining. In the literature, model assessment in the context of non-normal distributions has not yet received a lot of attention. Indeed, many existing model selection criteria such as the Bayes information criterion and C-p, may not be suitable for a situation in which the conditional mean and variance of the response are dependent, such as in generalized linear model regression. In this article we propose a new adaptive model selection criterion and construct an approximately unbiased Kullback-Leibler loss estimator for model assessment in the context of exponential family distributions. This permits comparing any arbitrary complex modeling procedures. Our proposal uses a concept called generalized degrees of freedom that generalizes the concept originally proposed for the normal distribution. The proposed procedure is implemented for the binomial and Poisson distributions and its small sample operating characteristics are examined via simulations. The usefulness of the method is demonstrated by an application to a study of the effect of air pollution on certain respiratory diseases. Numerical analyses support the utility of the methodology.