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Least squares theory for possibly singular models |
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| Authors: | C. Radhakrishna Rao |
| Abstract: | In a recent paper, Scobey (1975) observed that the usual least squares theory can be applied even when the covariance matrix σ2V of Y in the linear model Y = Xβ + e is singular by choosing the Moore-Penrose inverse (V+XX′)+ instead of V-1 when V is nonsingular. This result appears to be wrong. The appropriate treatment of the problem in the singular case is described. |
| Keywords: | Gauss-Markoff model singular multivariate normal generalized inverse least squares theory singular linear models Primary 62J05 secondary 15A09 |