Selection of smoothing parameters inB-spline nonparametric regression models using information criteria
Selection of smoothing parameters inB-spline nonparametric regression models using information criteria
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DOI：
10.1007/bf02523388
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发表时间：
2003-12
影响因子：
1
通讯作者：
S. Imoto;S. Konishi
中科院分区：
文献类型：
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作者：
S. Imoto;S. Konishi
我们考虑用最大惩罚似然法估计的B-样条非参数回归模型来从具有复杂非线性结构的数据中提取信息。B-Spline光顺的关键点是光顺参数和基函数的选择，基于交叉验证和Akaike信息准则(AIC)，已经提出了几个选择器。然而，可以注意到，AIC是用最大似然法估计的模型的评估标准，它是在假设真实分布属于指定的参数模型的情况下推导出来的。本文在模型误指定的广义线性模型的背景下，给出了用最大惩罚似然方法估计的B-样条非参数回归模型的信息准则。我们使用蒙特卡罗实验和真实的数据例子来检验我们的标准的性质，包括前面提出的各种选择器。
We consider the use ofB-spline nonparametric regression models estimated by the maximum penalized likelihood method for extracting information from data with complex nonlinear structure. Crucial points inB-spline smoothing are the choices of a smoothing parameter and the number of basis functions, for which several selectors have been proposed based on cross-validation and Akaike information criterion known as AIC. It might be however noticed that AIC is a criterion for evaluating models estimated by the maximum likelihood method, and it was derived under the assumption that the ture distribution belongs to the specified parametric model. In this paper we derive information criteria for evaluatingB-spline nonparametric regression models estimated by the maximum penalized likelihood method in the context of generalized linear models under model misspecification. We use Monte Carlo experiments and real data examples to examine the properties of our criteria including various selectors proposed previously.