Multivariate mode hunting: Data analytic tools with measures of significance

Multivariate mode hunting is of increasing practical importance. Only a few such methods exist, however, and there usually is a trade-off between practical feasibility and theoretical justification. In this paper we attempt to do both. We propose a method for locating isolated modes (or better, moda...

Full description

Saved in:
Bibliographic Details
Published in:Journal of multivariate analysis 2009-07, Vol.100 (6), p.1198-1218
Main Authors: Burman, Prabir, Polonik, Wolfgang
Format: Article
Language:English
Subjects:
62G20
62G20 Brownian bridge Distribution free Modality Nearest neighbor method Testing for antimodes VC-classes
62G99
62H99
62H99 secondary
Brownian bridge
Calibration
Combinatorics
Combinatorics. Ordered structures
Data analysis
Designs and configurations
Distribution free
Exact sciences and technology
Experimental design
Feasibility
Mathematics
Modality
Multivariate analysis
Nearest neighbor method
Nonparametric inference
primary
Probability and statistics
Sciences and techniques of general use
secondary
Statistics
Studies
Testing for antimodes
VC-classes
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Multivariate mode hunting is of increasing practical importance. Only a few such methods exist, however, and there usually is a trade-off between practical feasibility and theoretical justification. In this paper we attempt to do both. We propose a method for locating isolated modes (or better, modal regions) in a multivariate data set without pre-specifying their total number. Information on significance of the findings is provided by means of formal testing for the presence of antimodes. Critical values of the tests are derived from large sample considerations. The method is designed to be computationally feasible in moderate dimensions, and it is complemented by diagnostic plots. Since the null hypothesis under consideration is highly composite the proposed tests involve calibration in order to ensure a correct (asymptotic) level. Our methods are illustrated by application to real data sets.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2008.10.015