Post-hoc analyses in multiple regression based on prediction error

Rand R. Wilcox

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Post-hoc analyses in multiple regression based on prediction error

机译：基于预测误差的多元回归的事后分析

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A well-known problem in multiple regression is that it is possible to reject the hypothesis that all slope parameters are equal to zero, yet when applying the usual Student's T-test to the individual parameters, no significant differences are found. An alternative strategy is to estimate prediction error via the 0.632 bootstrap method for all models of interest and declare the parameters associated with the model that yields the smallest prediction error to differ from zero. The main results in this paper are that this latter strategy can have practical value versus Student's T; replacing squared error with absolute error can be beneficial in some situations and replacing least squares with an extension of the Theil-Sen estimator can substantially increase the probability of identifying the correct model under circumstances that are described.

机译：多元回归中的一个众所周知的问题是，有可能拒绝所有斜率参数等于零的假设，但是当对单个参数应用普通的Student T检验时，没有发现显着差异。一种替代策略是通过所有感兴趣模型的0.632引导程序方法估计预测误差，并声明与该模型相关联的参数，该参数产生的最小预测误差与零不同。本文的主要结果是，相对于学生的T，后一种策略具有实用价值。在某些情况下，用绝对误差替换平方误差可能是有益的，并且在描述的情况下，用Theil-Sen估计器的扩展替换最小二乘法可以大大增加识别正确模型的可能性。

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来源
《Journal of applied statistics》 |2008年第2期|9-17|共9页
作者
Rand R. Wilcox;
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作者单位

Department of Psychology, University of Southern California, Los Angeles, CA, USA;

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原文格式 PDF
正文语种 eng
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关键词
multiple comparisons; prediction error; bootstrap methods; robust regression;

机译：多重比较;预测误差引导方法;稳健回归;

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1. Post-hoc analyses in multiple regression based on prediction error [J] . Rand R. Wilcox Journal of applied statistics . 2008,第1期

机译：基于预测误差的多元回归的事后分析
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3. Adaptive error prediction method based on multiple linear regression for reversible data hiding [J] . Ma Bin, Wang Xiaoyu, Li Qi, Journal of Real-Time Image Processing . 2019,第4期

机译：基于多线性回归的自适应误差预测方法，可逆数据隐藏
4. Error Prediction Methods for Embedded Software Development Using Hybrid Models of Self-Organizing Maps and Multiple Regression Analyses [C] . Kazunori Iwata, Toyoshiro Nakashima, Yoshiyuki Anan, International conference on computer and information science . 2013

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5. Parameter estimates of interaction effects: Moderated multiple regression versus errors-in-variables regression [D] . Anderson, Lance E. 1989

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7. Basic Diagnosis and Prediction of Persistent Contrail Occurrence using High-resolution Numerical Weather Analyses/Forecasts and Logistic Regression. Part I: Effects of Random Error [O] . Duda David P., Minnis Patrick 2009

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Post-hoc analyses in multiple regression based on prediction error

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