Multivariate analysis of sample survey data

Abstract

Multivariate methods are used widely with sample survey data, yet the assumption of independently and identically distributed observations underlying many of these methods may be invalid for surveys of complex design. This thesis attempts to outline a formal statistical approach to this problem. A distinction is drawn between a disaggregated approach, where the aim is to model the data in relation to the structure of the population used in the sample design, and an aggregate approach where the target of inference is a population characteristic. Only the latter approach is considered. Most attention is given to the choice and properties of point estimators of a covariance matrix. In addition the estimation of correlation coefficients, regression coefficients, principal components and parameters in factor analysis is considered. Inference is mainly based an stochastic superpopulation models rather than on the classical randomisation distribution induced by a probability sampling design. The thesis divided into two parts. In the first part, a very general sample selection scheme depending on a set of design variables is combined with a rather restrictive classical super-population model in which units are independent with values distributed multivariatenormally. In the second part, a conventional two-stage sampling scheme is combined with a general superpopulation model for a clustered population.

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