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A General Solution for a Class of Weakly Constrained Linear Regression Problems

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge
Jos M. F. ten Berge*
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M. F. ten Berge, Vakgroep Psychologic, Rijksuniversiteit Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, The Netherlands.
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Abstract

This paper contains a globally optimal solution for a class of functions composed of a linear regression function and a penalty function for the sum of squared regression weights. Global optimality is obtained from inequalities rather than from partial derivatives of a Lagrangian function. Applications arise in multidimensional scaling of symmetric or rectangular matrices of squared distances, in Procrustes analysis, and in ridge regression analysis. The similarity of existing solutions for these applications is explained by considering them as special cases of the general class of functions addressed.

Keywords

squared distance scalingProcrustes analysisridge regression
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 4 , December 1991 , pp. 601 - 609
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

The author is obliged to Henk Kiers and Willem Heiser for helpful comments.

References

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