Some Methodological Aspects of Validation of Models in Nonparametric Regression
Some Methodological Aspects of Validation of Models in Nonparametric Regression
复制标题
非参数回归模型验证的一些方法论方面
DOI：
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发表时间：
2003
期刊：
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通讯作者：
A. Munk
中科院分区：
文献类型：
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作者：
H. Dette;A. Munk
本文介绍了在非参数回归模型中构造拟合优度检验的一些一般方法。我们主要关注的是开发统计方法来评估(验证)特定的参数模型ℳ，因为它们出现在各种应用领域。所有这些方法背后的基本思想是在假设特定模型(必须得到验证)以及在违反这一假设的广泛情况下都适用的假设下对某些拟合优度统计进行调查(这可能取决于特定的问题并且可能由不同的标准驱动)。这是因为经典假设的检验结果：“ℳ模型成立”(以及与之相关的p值)存在各种方法论缺陷。因此，我们的建议总是伴随着对第二类错误的分析来进行这样的测试，这是通常更严重的拟合度问题。我们给出了方法方面的描述，所需的渐近理论，并说明了检验模型假设的主要原则，如非参数回归模型中的特定参数形式或同方差。
In this paper we describe some general methods for constructing goodness of fit tests in nonparametric regression models. Our main concern is the development of statisticial methodology for the assessment (validation) of specific parametric models ℳ as they arise in various fields of applications. The fundamental idea which underlies all these methods is the investigation of certain goodness of fit statistics (which may depend on the particular problem and may be driven by different criteria) under the assumption that a specified model (which has to be validated) holds true as well as under a broad range of scenaria, where this assumption is violated. This is motivated by the fact that outcomes of tests for the classical hypothesis: “The model ℳ holds true” (and their associated p values) bear various methodological flaws. Hence, our suggestion is always to accompany such a test by an analysis of the type II error, which is in goodness of fit problems often the more serious one. We give a careful description of the methodological aspects, the required asymptotic theory, and illustrate the main principles in the problem of testing model assumptions such as a specific parametric form or homoscedasticity in nonparametric regression models.