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Nonparametric model selection: An approach based on density estimation.

机译：非参数模型选择：一种基于密度估计的方法。

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摘要

Model selection for regression and time series models can be regarded as a special kind of statistical inference. Any inference based on the assumption of a “true” model can be criticized. Model checking can help but often the diagnostics that are used for this purpose also assume a specific parameterization of the model. For this reason, despite their popularity and availability in statistical packages, criteria like the adjusted R-squared, Akaike's AIC, Sawa's BIC or Schwarz's BIC do not always produce the right answer and they should not be expected to. Nevertheless, if we use the definition of regression function as the conditional expectation of the response variable given a set of predictor variables, we can exploit our ability to estimate density functions consistently to derive a test for variable selection which is also consistent. In the dissertation two main approaches are suggested. The first one which uses the original response and predictors and that amounts to a test for conditional independence. The second one, on the contrary, uses the residuals from two nonparametric regression models and compares their estimated kernel density estimates using a distance between functions and is closer in spirit to the approach used in regression graphics. The approach based on the use of residuals, while weaker than the first one, can be easily extended to derive tests to perform model selection for nonnested models or to detect structural breaks in regression models.; None of these techniques can expect to escape the “curse of dimensionality”; nonetheless for the case of relatively simple models, basic simulations suggest that the technique is capable of producing good results.
机译：回归模型和时间序列模型的模型选择可以视为一种特殊的统计推断。任何基于“真实”模型假设的推论都会受到批评。模型检查可以提供帮助，但通常用于此目的的诊断还假设模型具有特定的参数设置。因此，尽管它们在统计软件包中很受欢迎并且可用，但是诸如调整后的R平方，Akaike的AIC，Sawa的BIC或Schwarz的BIC之类的标准并非总能得出正确的答案，因此不应期望它们会给出正确的答案。但是，如果使用回归函数的定义作为给定一组预测变量的响应变量的条件期望，则可以利用我们一致地估计密度函数的能力来得出变量选择的检验，该检验也应保持一致。本文提出了两种主要方法。第一个使用原始响应和预测变量，相当于条件独立性的检验。相反，第二个方法使用来自两个非参数回归模型的残差，并使用函数之间的距离比较它们的估计核密度估计值，并且在本质上更接近于回归图形中使用的方法。基于残差的使用方法虽然比第一种方法更弱，但可以轻松扩展以导出测试以对非嵌套模型进行模型选择或检测回归模型中的结构破坏。这些技术都无法逃脱“维数的诅咒”。尽管如此，对于相对简单的模型，基本的模拟表明该技术能够产生良好的结果。

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  • 作者

    Tiso, Maurizio.;

  • 作者单位

    University of Minnesota.;

  • 授予单位 University of Minnesota.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 1999
  • 页码 170 p.
  • 总页数 170
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 统计学;
  • 关键词

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