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S+ Functional Data Analysis: User’s Manual for Windows®

Douglas B. Clarkson Chris Fraley Charles C. Gu James O. Ramsey

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No disponible.

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2005 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-387-24969-8

ISBN electrónico

978-0-387-28393-7

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Insightful Corporation 2005

Tabla de contenidos

Introduction

Pp. 1-22

Basis Objects and Operations

Pp. 23-44

Functional Data Objects and Operations

Palabras clave: Functional Data; Linear Differential Operator; Basis Expansion; Univariate Base; Bivariate Function.

Pp. 45-69

Linear Differential Operators and Smoothing

Palabras clave: Penalty Function; Functional Data; Penalty Parameter; Height Data; Linear Differential Operator.

Pp. 71-86

Functional Registration

Pp. 87-99

Functional Linear Models

Palabras clave: Linear Regression Model; Gait Cycle; Final Height; Coefficient Function; Height Data.

Pp. 101-121

Functional Generalized Linear Models

Pp. 123-129

Functional Principal Components

Palabras clave: Harmonic Measure; Principal Component Score; Functional Principal Component Analysis; Functional Principal Component; Classical Principal Component Analysis.

Pp. 131-144

Canonical Correlation

Pp. 145-153

Functional Cluster Analysis

Cluster analysis is an exploratory technique. Functional data methods offer the advantage of allowing a greater variety of clustering matrixes to choose from. The examples involving the clustering of Canadian weather stations are meant to be illustrative, since the known locations of weather stations can be used to infer which ones should exhibit similar weather patterns. The objective is not so much to find “real” clusters of stations, but rather to learn how the weather patterns at the different stations are related. Some of the clusters obtained consist of stations that are located in the same region, which we would expect similar to have weather patterns. Other aspects of the clustering are harder to interpret (e.g., assignment of Prince Rupert and Halifax to the same cluster), although they may also indicate relationships in weather patterns for stations at some distance from each other. A cluster analysis that accounted for both precipitation and temperature (and other weather related variables such as humidity) might be preferable, provided a suitable clustering metric could be found. Methods for determining the number of clusters in functional cluster analysis are identical to those in the classical case, and thus are not discussed further here. If groupings for some of the data are known in advance, it may be preferable to use a discriminant function analysis to find the variables and matrix that best classify the remaining observations. In the chapter on functional generalized linear models, we use a form of discriminant function analysis, functional logistic models, to classify the weather stations.

Palabras clave: Hierarchical Cluster Analysis; Daily Precipitation; Weather Pattern; Average Daily Temperature; Discriminant Function Analysis.

Pp. 155-164