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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/15668 |
| Date | January 1982 |
| Creators | Dunne, Timothy Terence |
| Contributors | Troskie, Casper G |
| Publisher | University of Cape Town, Faculty of Science, Department of Statistical Sciences |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Doctoral Thesis, Doctoral, PhD |
| Format | application/pdf |
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