The University of Southampton
University of Southampton Institutional Repository

The effect of selection on the robustness of multivariate methods

The effect of selection on the robustness of multivariate methods
The effect of selection on the robustness of multivariate methods

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)

University of Southampton
Holmes, David John
Holmes, David John

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

Record type: Thesis (Doctoral)

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)

This record has no associated files available for download.

More information

Published date: 1987

Identifiers

Local EPrints ID: 461679
URI: http://eprints.soton.ac.uk/id/eprint/461679
PURE UUID: ec15875e-575d-4f9d-8616-c9d058ff12ab

Catalogue record

Date deposited: 04 Jul 2022 18:52
Last modified: 04 Jul 2022 18:52

Export record

Contributors

Author: David John Holmes

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×