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Functional data analysis with applications in biostatistics

thesis
posted on 29.03.2022, 02:41 by Sarah Jane Ratcliffe
Functional data analysis is concerned with the analysis of data for which the observed responses for each subject are continuous curves. In practice measurements are taken at discrete time points but estimates are required over the entire time interval. Traditional techniques for analysis of multiple curves such as longitudinal data analysis or time series methods are unsuitable for this type of data since there are generally more measurements per subject than subjects and stationarity assumptions do not necessarily hold. With a technology induced growth in data of this kind research into techniques for functional data analysis has become an emerging area in recent years. This thesis aims to develop new techniques for functional data analysis focusing on three problems: logistic regression with a functional regressor, linear and logistic regression for a repeatedly stimulated functional regressor, and a functional mixed-effects type model for joint mean and covariance modelling. For each of the problems, we develop solutions using a basis function approach, that is, expressing the data for each subject as a linear combination of known basis functions. Using this approach we are able to overcome singularity problems associated with having more measurements than subjects. As well as calculating maximum likelihood or least squares parameter estimates model diagnostic and smoothing parameter selection issues are addressed. The techniques developed in this thesis are applied to novel biostatistical data sets electroencephalographic data and fetal heart rate data. Of main interest is the fetal heart rate data which motivated the development of the regression techniques for a repeatedly stimulated functional parameter. It was found that the stimulated fetal heart rates could be used to predict an infant's risk category at birth and psychomotor development at 18 months of age. Most of the material presented in the thesis is my own work. The exception is: the work described in Section 6.3 is partly due to Victor Solo.

History

Table of Contents

Introduction -- Technical background -- Functional logistic regression -- Functional data with a repeated stimulus -- The fetal heart rate data -- Functional mean and covariance modelling -- Conclusion.

Notes

"October 2000". Bibliography: leaves 130-142 "Submitted in fulfilment of the requirement for the degree of Doctor of Philosophy in the Department of Statistics, Division of Economic and Financial Studies, Macquarie University".

Awarding Institution

Macquarie University

Degree Type

Thesis PhD

Degree

Thesis (PhD), Macquarie University, Division of Economic and Financial Studies, Dept. of Statistics

Department, Centre or School

Dept. of Statistics

Year of Award

2000

Principal Supervisor

Victor Solo

Additional Supervisor 1

Gillian Heller

Rights

Copyright disclaimer: http://www.copyright.mq.edu.au/ Copyright Sarah Ratcliffe 2000

Language

English

Extent

1 online resource (x, 142 p.) ill

Former Identifiers

mq:20315 http://hdl.handle.net/1959.14/176925 1654585