Estimating and depicting the structure of a distribution of random functions

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Estimating and depicting the structure of a distribution of random functions

TitleEstimating and depicting the structure of a distribution of random functions
Publication TypeJournal Article
Year of Publication2002
AuthorsHall, P, Heckman, NE
JournalBIOMETRIKA
Volume89
Pagination145-158
Date PublishedMAR
Type of ArticleArticle
ISSN0006-3444
Keywordsbandwidth, cluster analysis, Functional data analysis, Gaussian process, generalised Fourier expansion, Karhunen-Loeve expansion, kernel methods, line of steepest ascent, mode, nonparametric density estimation, tree diagram
AbstractWe suggest a nonparametric approach to making inference about the structure of distributions in a potentially infinite-dimensional space, for example a function space, and displaying information about that structure. It is suggested that the simplest way of presenting the structure is through modes and density ascent lines, the latter being the projections into the sample space of the curves of steepest ascent up the surface of a functional-data density. Modes are always points in the sample space, and ascent lines are always one-parameter structures, even when the sample space is determined by an infinite number of parameters. They are therefore relatively easily depicted. Our methodology is based on a functional form of an iterative data-sharpening algorithm.
DOI10.1093/biomet/89.1.145