Browsing by Author "Coutsourides, Dimitris"

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    A detailed investigation of the linear model and some of its underlying assumptions
    (1977) Coutsourides, Dimitris; Troskie, Casper G
    The purpose of this thesis is to provide a study of the linear model. The whole work has been split into 6 chapters. In Chapter 1 we define and examine the two linear models, i.e. the regression and the correlation model. More specifically we show that the regression model is the conditional version of the correlation model. In Chapter 2 we deal with the problem of multicollinearity. We investigate the sources of near singularities, we give some methods of detecting the multicollinearity, and we state briefly methods for overcoming this problem. In Chapter 3 we consider the least squares method with restrictions, and we dispose of some tests for testing the linear restrictions. The theory concerning the sign of least squares estimates is discussed, then we deal with the method for augmenting existing data. Chapter 4 is mainly devoted to ridge regression. We state methods for selecting the best estimate for k. Some extensions are given dealing with the shrinkage estimators and the linear transforms of the least squares. In Chapter 5 we deal with the principal components, and we give methods for selecting the best subset of principal components. Much attention was given to a method called fractional rank and latent root regression analysis. In Chapter 6 comparisons were performed between estimators previously mentioned. Finally the conclusions are stated.
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    Distributions of certain test statistics in multivariate regression
    (1980) Coutsourides, Dimitris; Troskie, Casper G
    This thesis is principally concerned with test criteria for testing different hypotheses for the multivariate regression. In this preface a brief summary of each of the succeeding chapters is given. In Chapter 1 the problem of testing the equality of two population multiple correlation coefficients in identical regression experiments has been studied. The author's results are extentions to those of Schuman and Bradley. In Chapter 2 the results of Chapter 1 are extended to the multivariate case, in other words, the author has constructed tests in order to test the equality of two population generalized multiple correlation matrices. In Chapter 3 the author shows that the Ridge Regression, Principal Components and Shrunken estimators yield the same central t and F statistics as the ordinary least square estimator. In Chapter 4 using the results of Aitken, simultaneous tests for the Cp-criterion of Mallows are constructed. Some comments on extrapolation and prediction are made. In Chapter 5 the Ridge and Principal components residuals are studied. Their use for detecting outliers, when multi-collinearity is present, is examined.