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Discontinuous Parameter Estimates With Least Squares Estimators, J. L. Mead
Discontinuous Parameter Estimates With Least Squares Estimators, J. L. Mead
Mathematics Faculty Publications and Presentations
We discuss weighted least squares estimates of ill-conditioned linear inverse problems where weights are chosen to be inverse error covariance matrices. Least squares estimators are the maximum likelihood estimate for normally distributed data and parameters, but here we do not assume particular probability distributions. Weights for the estimator are found by ensuring its minimum follows a χ2 distribution. Previous work with this approach has shown that it is competitive with regularization methods such as the L-curve and Generalized Cross Validation (GCV) [20]. In this work we extend the method to find diagonal weighting matrices, rather than a scalar regularization …