Regularization and the general Gauss-Markov linear model

Authors:
Hong Yuan Zha and Per Christian Hansen

Journal:
Math. Comp. **55** (1990), 613-624

MSC:
Primary 65F20; Secondary 15A06, 65F30

DOI:
https://doi.org/10.1090/S0025-5718-1990-1035946-9

MathSciNet review:
1035946

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Abstract | References | Similar Articles | Additional Information

Abstract: If the coefficient matrix in the general Gauss-Markov linear model is ill-conditioned, then the solution is very sensitive to perturbations. For such problems, we propose to add Tikhonov regularization to the model, and we show that this actually stabilizes the solution and decreases its variance. We also give a numerically stable algorithm for computing the regularized solution efficiently.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1990-1035946-9

Keywords:
Estimation in the general Gauss-Markov linear model,
Tikhonov regularization,
restricted SVD,
discrete Picard condition

Article copyright:
© Copyright 1990
American Mathematical Society