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A Generalized View on Continuum Regression

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  • Anders Björkström
  • Rolf Sundberg

Abstract

ABSTRACT. We generalize the relationship between continuum regression (Stone & Brooks, 1990) and ridge regression, by showing that any optimization principle will yield a regressor proportional to a ridge regressor, provided only that the principle implies maximizing a function of the regressor’s sample correlation coefficient and its sample variance. This relationship shows that continuum regression as defined via ridge regression (“least squares ridge regression”) is a more generally valid methodology than previously realized, and also opens up for alternative choices of its second and subsequent factors.

Suggested Citation

  • Anders Björkström & Rolf Sundberg, 1999. "A Generalized View on Continuum Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 17-30, March.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:1:p:17-30
    DOI: 10.1111/1467-9469.00134
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    Cited by:

    1. Čížek, Pavel, 2004. "(Non) Linear Regression Modeling," Papers 2004,11, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    2. Jung, Sungkyu, 2018. "Continuum directions for supervised dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 27-43.

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