Doctoral Degrees (Statistics and Actuarial Science)

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Influential data cases when the C-p criterion is used for variable selection in multiple linear regression
(Stellenbosch : Stellenbosch University, 2003) Uys, Daniel Wilhelm; Steel, S. J.; Van Vuuren, J. O.; Stellenbosch University. Faculty of Economic and Management Sciences . Dept. of Statistical and Actuarial Science.
ENGLISH ABSTRACT: In this dissertation we study the influence of data cases when the Cp criterion of Mallows (1973) is used for variable selection in multiple linear regression. The influence is investigated in terms of the predictive power and the predictor variables included in the resulting model when variable selection is applied. In particular, we focus on the importance of identifying and dealing with these so called selection influential data cases before model selection and fitting are performed. For this purpose we develop two new selection influence measures, both based on the Cp criterion. The first measure is specifically developed to identify individual selection influential data cases, whereas the second identifies subsets of selection influential data cases. The success with which these influence measures identify selection influential data cases, is evaluated in example data sets and in simulation. All results are derived in the coordinate free context, with special application in multiple linear regression.