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Three Steps Towards Robust Regression

Published online by Cambridge University Press:  01 January 2025

Howard Wainer  and
David Thissen
Howard Wainer*
Affiliation:
The University of Chicago
David Thissen
Affiliation:
The University of Chicago
*
Requests for reprints should be sent to Howard Wainer, 5848 University Avenue, Chicago, Illinois 60637.
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Abstract

The three most commonly used statistics, the arithmetic mean, variance, and the product-moment correlation, are most unfortunate choices when data are not strictly Gaussian. A new measure of correlation and a measure of scale are proposed which are substantially more robust than their least squares counterparts. An illustration shows how increased robustness can be obtained through the use of equal regression weights without severe loss in accuracy. The paper also shows how incorporating knowledge about the theoretical structure of the regression coefficients into their estimation can aid substantially in increasing their robustness.

Keywords

Regression CoefficientPublic PolicyStatistical TheoryRegression WeightSevere Loss
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 1 , March 1976 , pp. 9 - 34
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

Various aspects of the research reported here was supported by: NICH and HD grant 1 R01 HD08896-01 AFY to The University of Chicago, Howard Wainer, Principal Investigator; The Social Sciences Divisional Research Grants of the University of Chicago; NIH grant HD-04660 and contract NICHD-72-2735 to the Fels Research Institute, A. F. Roche, Principal Investigator.

We wish to thank John W. Tukey for his initial help and continuing interest. The measure of correlation (rt) and the resistant measure of scale herein proposed stem directly from a suggestion by Professor Tukey. Additionally, we wish to acknowledge the help and useful suggestions of W. Kruskal, A. F. Roche, J. Kettenring, and R. Gnanadesikan.

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