Universität zu Köln

Mosler, Karl and Mozharovskyi, Pavlo (2017). Fast DD-classification of functional data. Stat. Pap., 58 (4). S. 1055 - 1090. NEW YORK: SPRINGER. ISSN 1613-9798

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Abstract

A fast nonparametric procedure for classifying functional data is introduced. It consists of a two-step transformation of the original data plus a classifier operating on a low-dimensional space. The functional data are first mapped into a finite-dimensional location-slope space and then transformed by a multivariate depth function into the DD-plot, which is a subset of the unit square. This transformation yields a new notion of depth for functional data. Three alternative depth functions are employed for this, as well as two rules for the final classification in . The resulting classifier has to be cross-validated over a small range of parameters only, which is restricted by a Vapnik-Chervonenkis bound. The entire methodology does not involve smoothing techniques, is completely nonparametric and allows to achieve Bayes optimality under standard distributional settings. It is robust, efficiently computable, and has been implemented in an R environment. Applicability of the new approach is demonstrated by simulations as well as by a benchmark study.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Mosler, Karl UNSPECIFIED UNSPECIFIED UNSPECIFIED Mozharovskyi, Pavlo UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-210650
DOI:	10.1007/s00362-015-0738-3
Journal or Publication Title:	Stat. Pap.
Volume:	58
Number:	4
Page Range:	S. 1055 - 1090
Date:	2017
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1613-9798
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DEPTH Multiple languages Statistics & Probability Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/21065