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Title: Estimating large-scale general linear and seemingly unrelated regressions models after deleting observations
Authors: Hadjiantoni, Stella 
Kontoghiorghes, Erricos John 
Keywords: Downdating
Generalized least squares
Seemingly unrelated regressions
Singular dispersion matrix
Issue Date: 27-Jan-2016
Source: Statistics and Computing 27 January 2016, Pages 1-13
Abstract: A new numerical method to solve the downdating problem (and variants thereof), namely removing the effect of some observations from the generalized least squares (GLS) estimator of the general linear model (GLM) after it has been estimated, is extensively investigated. It is verified that the solution of the downdated least squares problem can be obtained from the estimation of an equivalent GLM, where the original model is updated with the imaginary deleted observations. This updated GLM has a non positive definite dispersion matrix which comprises complex covariance values and it is proved herein to yield the same normal equations as the downdated model. Additionally, the problem of deleting observations from the seemingly unrelated regressions model is addressed, demonstrating the direct applicability of this method to other multivariate linear models. The algorithms which implement the novel downdating method utilize efficiently the previous computations from the estimation of the original model. As a result, the computational cost is significantly reduced. This shows the great usability potential of the downdating method in computationally intensive problems. The downdating algorithms have been applied to real and synthetic data to illustrate their efficiency.
ISSN: Springer New York LLC
Rights: © 2016 Springer Science+Business Media New York
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