Function Estimation and Functional Data Analysis

BW Silverman

doi:10.1007/978-3-0348-9112-7_17

Function Estimation and Functional Data Analysis

BW Silverman

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

Abstract

The roughness penalty method is widely used in function estimation, and is closely related to methods of regularization well known in numerical analysis. Some background to the development of this method is discussed. The versatility of the method is illustrated by its application to an unusual smoothing problem, involving the estimation of a branching system of curves. The second main focus of the paper is on problems where the data are themselves functions, an area known as functional data analysis. The roughness penalty method is a key component of extensions to the functional context of principal components analysis and canonical correlation analysis. These techniques are described and contrasted, and are illustrated by reference to a set of data on the development of human gait.

Translated title of the contribution	Function estimation and functional data analysis
Original language	English
Title of host publication	First European Congress of Mathematics Paris, July 6–10, 1992
Subtitle of host publication	Vol. II: Invited Lectures (Part 2)
Publisher	Birkhäuser Basel
Pages	407-427
Number of pages	21
Volume	2
ISBN (Electronic)	9783034891127
ISBN (Print)	9783034899123
DOIs	https://doi.org/10.1007/978-3-0348-9112-7_17
Publication status	Published - 1994

Publication series

Name	Progress in Mathematics
Publisher	Springer
Volume	120
ISSN (Print)	0743-1643

Bibliographical note

Publisher: Birkhäuser Verlag, Basel
Other: Eds. A.Joseph, F.Mignot, F.Murat, B.Prum and R.Rentschler

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10.1007/978-3-0348-9112-7_17

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abstract = "The roughness penalty method is widely used in function estimation, and is closely related to methods of regularization well known in numerical analysis. Some background to the development of this method is discussed. The versatility of the method is illustrated by its application to an unusual smoothing problem, involving the estimation of a branching system of curves. The second main focus of the paper is on problems where the data are themselves functions, an area known as functional data analysis. The roughness penalty method is a key component of extensions to the functional context of principal components analysis and canonical correlation analysis. These techniques are described and contrasted, and are illustrated by reference to a set of data on the development of human gait.",

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N2 - The roughness penalty method is widely used in function estimation, and is closely related to methods of regularization well known in numerical analysis. Some background to the development of this method is discussed. The versatility of the method is illustrated by its application to an unusual smoothing problem, involving the estimation of a branching system of curves. The second main focus of the paper is on problems where the data are themselves functions, an area known as functional data analysis. The roughness penalty method is a key component of extensions to the functional context of principal components analysis and canonical correlation analysis. These techniques are described and contrasted, and are illustrated by reference to a set of data on the development of human gait.

AB - The roughness penalty method is widely used in function estimation, and is closely related to methods of regularization well known in numerical analysis. Some background to the development of this method is discussed. The versatility of the method is illustrated by its application to an unusual smoothing problem, involving the estimation of a branching system of curves. The second main focus of the paper is on problems where the data are themselves functions, an area known as functional data analysis. The roughness penalty method is a key component of extensions to the functional context of principal components analysis and canonical correlation analysis. These techniques are described and contrasted, and are illustrated by reference to a set of data on the development of human gait.

U2 - 10.1007/978-3-0348-9112-7_17

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M3 - Conference Contribution (Conference Proceeding)

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T3 - Progress in Mathematics

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BT - First European Congress of Mathematics Paris, July 6–10, 1992

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