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Contributions to the theory of generalized inverses, the linear model and outliers

Column-space conditions are shown to be at the heart of a number of identities linking generalized inverses of rectangular matrices. These identities give some new insights into reparametrizations of the general linear model, and into the imposition of constraints, when the variance-covariance structure is σ².I. Hypothesis-test statistics for non-estimable functions are shown to give no further information than underlying estimable functions. For an arbitrary variance-covariance structure the "sweep-out" method is generalized. The John and Draper model for outliers is extended, and distributional results established. Some diagnostic statistics for outlying or influential observations are considered. A Bayesian formulation of outliers in the general linear model is attempted.
Date January 1982
CreatorsDunne, Timothy Terence
ContributorsTroskie, Casper G
PublisherUniversity of Cape Town, Faculty of Science, Department of Statistical Sciences
Source SetsSouth African National ETD Portal
Detected LanguageEnglish
TypeDoctoral Thesis, Doctoral, PhD

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