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Optimal and efficient experimental design for nonparametric regression with application to functional data

Optimal and efficient experimental design for nonparametric regression with application to functional data
Optimal and efficient experimental design for nonparametric regression with application to functional data
Functional data is ubiquitous in modern science, technology and medicine. An example, which motivates the work in this thesis, is an experiment in tribology to investigate wear in automotive transmission.

The research in this thesis provides methods for the design of experiments when the response is assumed to be a realisation of a smooth function. In the course of the research, two areas were investigated: designs for local linear smoothers and designs for discriminating between two functional linear models.

Designs that are optimal for minimising the prediction variance of a smooth function were found across an interval using two kernel smoothing methods: local linear regression and Gasser and Muller estimation. The values of the locality parameter and run size were shown to affect the optimal design. Optimal designs for best prediction using local linear regression were applied to the tribology experiment. A compound optimality criterion is proposed which is a weighted average of the integrated prediction variance and the inverse of the trace of the smoothing matrix using the Gasser and Muller estimator. The complexity of the model to be fitted was shown to influence the selection of optimal design points. The robustness of these optimal designs to misspecification of the kernel function for the compound criterion was also critically assessed.

A criterion and method for finding T-optimal designs was developed for discriminating between two competing functional linear models. It was proved that the choice of optimal design is independent of the parameter values when discriminating between two nested functional linear models that differ by only one term. The performance of T-optimal designs was evaluated in simulation studies which calculated the power of the test for assessing the fit of one model using data generated from the competing model.
Fisher, Verity
410a29f9-7309-4235-9bb7-2590b1264405
Fisher, Verity
410a29f9-7309-4235-9bb7-2590b1264405
Woods, David
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Lewis, Susan
a69a3245-8c19-41c6-bf46-0b3b02d83cb8

(2012) Optimal and efficient experimental design for nonparametric regression with application to functional data. University of Southampton, Mathematical Sciences, Doctoral Thesis, 192pp.

Record type: Thesis (Doctoral)

Abstract

Functional data is ubiquitous in modern science, technology and medicine. An example, which motivates the work in this thesis, is an experiment in tribology to investigate wear in automotive transmission.

The research in this thesis provides methods for the design of experiments when the response is assumed to be a realisation of a smooth function. In the course of the research, two areas were investigated: designs for local linear smoothers and designs for discriminating between two functional linear models.

Designs that are optimal for minimising the prediction variance of a smooth function were found across an interval using two kernel smoothing methods: local linear regression and Gasser and Muller estimation. The values of the locality parameter and run size were shown to affect the optimal design. Optimal designs for best prediction using local linear regression were applied to the tribology experiment. A compound optimality criterion is proposed which is a weighted average of the integrated prediction variance and the inverse of the trace of the smoothing matrix using the Gasser and Muller estimator. The complexity of the model to be fitted was shown to influence the selection of optimal design points. The robustness of these optimal designs to misspecification of the kernel function for the compound criterion was also critically assessed.

A criterion and method for finding T-optimal designs was developed for discriminating between two competing functional linear models. It was proved that the choice of optimal design is independent of the parameter values when discriminating between two nested functional linear models that differ by only one term. The performance of T-optimal designs was evaluated in simulation studies which calculated the power of the test for assessing the fit of one model using data generated from the competing model.

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Published date: December 2012
Organisations: University of Southampton, Mathematical Sciences

Identifiers

Local EPrints ID: 358623
URI: http://eprints.soton.ac.uk/id/eprint/358623
PURE UUID: 441ac1c5-7eee-45fa-9a1b-19841f673f8b
ORCID for David Woods: ORCID iD orcid.org/0000-0001-7648-429X

Catalogue record

Date deposited: 10 Dec 2013 11:59
Last modified: 19 Jun 2019 00:37

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Contributors

Author: Verity Fisher
Thesis advisor: David Woods ORCID iD
Thesis advisor: Susan Lewis

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