The University of Southampton
University of Southampton Institutional Repository

Optimal design for prediction using local linear regression and the DSI-criterion

Optimal design for prediction using local linear regression and the DSI-criterion
Optimal design for prediction using local linear regression and the DSI-criterion
When it is anticipated that data to be collected from an experiment cannot be adequately described by a low-order polynomial, alternative modelling and new design methods are required. Local linear regression, where the response is approximated locally by a series of weighted linear regressions, is an effective nonparametric smoothing method that makes few assumptions about the functional form of the response. We present new methods for the optimal design of experiments for local linear regression, including a new criterion, called DSI-optimality, to find designs that enable precise prediction across a continuous interval. Designs are found numerically for weights defined through the Gaussian and uniform kernels. Theoretical results are presented for the uniform kernel and the special case of prediction at a single point. The sensitivity of the designs to the choice of bandwidth in the local linear regression is studied, and it is found that designs for the Gaussian kernel with large bandwidth have a small number of distinct design points. The methodology is motivated by, and demonstrated on, an experiment from Tribology.
33-54
Fisher, Verity A.
5c3122fb-1397-4347-aa0d-b887565727fe
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Lewis, Susan M.
a69a3245-8c19-41c6-bf46-0b3b02d83cb8
Fisher, Verity A.
5c3122fb-1397-4347-aa0d-b887565727fe
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Lewis, Susan M.
a69a3245-8c19-41c6-bf46-0b3b02d83cb8

Fisher, Verity A., Woods, David C. and Lewis, Susan M. (2013) Optimal design for prediction using local linear regression and the DSI-criterion. Statistics and Applications, 11 (1 & 2), 33-54.

Record type: Article

Abstract

When it is anticipated that data to be collected from an experiment cannot be adequately described by a low-order polynomial, alternative modelling and new design methods are required. Local linear regression, where the response is approximated locally by a series of weighted linear regressions, is an effective nonparametric smoothing method that makes few assumptions about the functional form of the response. We present new methods for the optimal design of experiments for local linear regression, including a new criterion, called DSI-optimality, to find designs that enable precise prediction across a continuous interval. Designs are found numerically for weights defined through the Gaussian and uniform kernels. Theoretical results are presented for the uniform kernel and the special case of prediction at a single point. The sensitivity of the designs to the choice of bandwidth in the local linear regression is studied, and it is found that designs for the Gaussian kernel with large bandwidth have a small number of distinct design points. The methodology is motivated by, and demonstrated on, an experiment from Tribology.

Text
fwl.pdf - Accepted Manuscript
Download (500kB)

More information

Published date: 2013
Organisations: Statistical Sciences Research Institute

Identifiers

Local EPrints ID: 361127
URI: http://eprints.soton.ac.uk/id/eprint/361127
PURE UUID: bac9e17a-46bc-4efb-ac11-37862f84371e
ORCID for David C. Woods: ORCID iD orcid.org/0000-0001-7648-429X

Catalogue record

Date deposited: 15 Jan 2014 13:40
Last modified: 15 Mar 2024 03:05

Export record

Contributors

Author: Verity A. Fisher
Author: David C. Woods ORCID iD
Author: Susan M. Lewis

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.

×