Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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An Explicit Solution for Multivariate Ridge Regression

  • Shin, Min-Woong (Department of Mathematics, Hankuk University of Foreign Studies) ;
  • Park, Sung H. (Department of Computer Science and Statistics, Seoul National University)
  • Published : 1982.06.01
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Abstract

We propose that, in order to control the inflation and general instability associated with the least squares estimates, we can use the ridge estimator $$ \hat{B}^* = (X'X+kI)^{-1}X'Y : k \leq 0$$ for the regression coefficients B in multivariate regression. Our hope is that by accepting some bias, we can achieve a larger reduction in variance. We show that such a k always exists and we derive the formula obtaining k in multivariate ridge regression.

Keywords

References

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