The effect of selection on the robustness of multivariate methods

Holmes, David John (1987) The effect of selection on the robustness of multivariate methods. University of Southampton, Doctoral Thesis.

Abstract

This thesis is concerned with the multivariate analysis of survey data collected via a complex sample design. It is assumed that the selection of the sample depends on the population values of a vector of auxiliary (design) variables Z atop ∼ which are related to the survey variables of interest X atop ∼. Conventional (standard) estimators, based on the assumption of simple random sampling, are inappropriate, and alternative procedures which take into account the information carried by the sample should be used. A model-based procedure, which adjusts for the effects of selection, has been proposed. Under a superpopulation model in which units are independent and the regression of X atop ∼ on Z atop ∼ is linear and homoscedastic, these adjusted estimators perform well - they are maximum likelihood estimators if (X atop ∼ Z atop ∼) are multivariate normal. We examine the sensitivity/robustness of this model-based adjustment when the underlying assumptions are violated, by systematically considering failure of the linearity assumption and the homoscedasticity assumption separately. It is shown that the adjusted estimator can be very sensitive to the assumptions underlying its derivation and that alternative estimators, which combine model-based ideas with the design-based property of being design-consistent, are more appropriate. These estimation procedures are compared in the context of correlation analysis, principal component analysis, canonical correlation analysis and regression analysis. The validity of our theoretical results is assessed in a series of simulation studies based on a variety of stratified sampling designs. (D80993)

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