Browsing by Author "Dunne, Timothy Terence"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Open Access
    Contributions to the theory of generalized inverses, the linear model and outliers
    (1982) Dunne, Timothy Terence; Troskie, Casper G
    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.
  • Thumbnail Image
    Item
    Open Access
    Outliers and influence under arbitrary variance
    (1986) Schall, Robert; Dunne, Timothy Terence
    Using a geometric approach to best linear unbiased estimation in the general linear model, the additional sum of squares principle, used to generate decompositions, can be generalized allowing for an efficient treatment of augmented linear models. The notion of the admissibility of a new variable is useful in augmenting models. Best linear unbiased estimation and tests of hypotheses can be performed through transformations and reparametrizations of the general linear model. The theory of outliers and influential observations can be generalized so as to be applicable for the general univariate linear model, where three types of outlier and influence may be distinguished. The adjusted models, adjusted parameter estimates, and test statistics corresponding to each type of outlier are obtained, and data adjustments can be effected. Relationships to missing data problems are exhibited. A unified approach to outliers in the general linear model is developed. The concept of recursive residuals admits generalization. The typification of outliers and influential observations in the general linear model can be extended to normal multivariate models. When the outliers in a multivariate regression model follow a nested pattern, maximum likelihood estimation of the parameters in the model adjusted for the different types of outlier can be performed in closed form, and the corresponding likelihood ratio test statistic is obtained in closed form. For an arbitrary outlier pattern, and for the problem of outliers in the generalized multivariate regression model, three versions of the EM-algorithm corresponding to three types of outlier are used to obtain maximum likelihood estimates iteratively. A fundamental principle is the comparison of observations with a choice of distribution appropriate to the presumed type of outlier present. Applications are not necessarily restricted to multivariate normality.
  • Thumbnail Image
    Item
    Open Access
    Statistical investigation into academic performance in the Faculty of Science at the University of Cape Town in the period 1990-1997
    (1999) Ronda, Katarzyna; Dunne, Timothy Terence; Troskie, Casper G
    Ultimate academic success at any tertiary institution is affected and partially determined by many factors related to various aspects of individual's life. These factors could be separated into the following distinct categories, namely, educational, biographical, environmental and personal factors. Some of these determinants are used in the admission procedures adopted at tertiary institutions. In South Africa, the results of different final matriculation examinations (referred to as matric or matric exams) written in several educational departments throughout the country are employed to assess the individual's potential to succeed. However, effectiveness of matric results as predictors of successful academic performance has always been controversial. Expressing these concerns and desiring to explore them, the Faculty of Science at the University of Cape Town (UCT) accepted a proposal from the Department of Statistical Sciences to investigate several issues affecting students' performance in the Faculty. The proposal has led to developing this M.Sc. thesis. The major issue of concern in this study is to describe, on a retrospective basis, the extent to which the current selection criteria based on the matric results may have predicted various types of academic performance in the Faculty amongst those selected and admitted. The thesis also exhibits a coherent and fairly complete methodology that is applicable at general or at particular levels of student performance data analysis on a continuing year-to-year basis. The particular statistical methods and techniques in this study have been summarised and discussed in the three Appendices.