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Statistical inference for a robust measure of multiple correlation. (English) Zbl 1446.62012

Härdle, Wolfgang (ed.) et al., COMPSTAT. Proceedings in computational statistics. 15th symposium, Berlin, Germany, August 24–28, 2002. Heidelberg: Physica-Verlag. 557-562 (2002).
Summary: In regression analysis it is standard practice to report an R-squared statistic. This measure of multiple correlation is based on the Least Squares estimator, which is known to be extremely sensitive to outliers. The associated R-squared suffers from the same lack of robustness. Also the value of the F-statistic, used to see whether the explanatory variables have jointly a significant influence on the dependent variable, exhibits similar problems. Many robust estimation procedures are available now, but there has been less emphasis on the development of the inference part and in particular on the study of robust R-squared measures. It is however clear that applied statisticians desire to have the same tools to validate their model as when using the classical least squares estimator. In this note we will study the stability properties of robust measures of multiple correlation, and also investigate the size and power of F-statistics based on them.
For the entire collection see [Zbl 1023.00020].

MSC:

62-08 Computational methods for problems pertaining to statistics
62J05 Linear regression; mixed models
62F35 Robustness and adaptive procedures (parametric inference)
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References:

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