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On the mean square error associated with adaptive generalized ridge regression

Geoffrey J. McLachlan

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Abstract

Abstract Some numerical results are presented for generalized ridge regression where the additive constants are based on the data. The adaptive estimator so obtained is compared with the least‐squares estimator on the basis of mean square error (MSE). It is shown that the MSE of each component of the vector of ridge estimators may be as low as 47.1% of the variance of the corresponding component of the least squares vector or as high as 125.2%.

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What this paper is about

Abstract Some numerical results are presented for generalized ridge regression where the additive constants are based on the data. The adaptive estimator so obtained is compared with the least‐squares estimator on the basis of mean square error (MSE). It is shown that the MSE of each component of the vector of ridge estimators may be as low as 47.1% of the variance of the corresponding component of the least squares vector or as high as 125.2%.

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Available abstract

Abstract Some numerical results are presented for generalized ridge regression where the additive constants are based on the data. The adaptive estimator so obtained is compared with the least‐squares estimator on the basis of mean square error (MSE). It is shown that the MSE of each component of the vector of ridge estimators may be as low as 47.1% of the variance of the corresponding component of the least squares vector or as high as 125.2%.

Key concepts: Mathematics, Mean squared error, Estimator, Ridge, Statistics, Generalized least squares, Least-squares function approximation, Basis (linear algebra)

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