Graph-theoretic multisample tests of equality in distribution for high dimensional data

Adam Petrie

Computational Statistics & Data Analysis, 2016, vol. 96, issue C, 145-158

Abstract: Testing whether two or more independent samples arise from a common distribution is a classic problem in statistics. Several multivariate two-sample tests of equality are based on graphs such as the minimum spanning tree, nearest neighbor, and optimal nonbipartite perfect matching. Here, the samples are pooled and the test statistic is the number of edges in the graph that connect points with different sample identities. These tests are typically unbiased and perform well when estimates of underlying probability densities are poor. However, these tests have not been thoroughly studied when data is very high dimensional or in the multisample case. We introduce the use of orthogonal perfect matchings for testing equality in distribution. A suite of Monte Carlo simulations on artificial and real data shows that orthogonal perfect matchings and spanning trees typically have higher power than other graphs and are also more effective at discerning when samples have differences in their covariance structure compared to other nonparametric tests such as the energy and triangle tests.

Keywords: Multisample problem; Perfect matching; Minimum spanning tree; Nearest neighbor; Energy; Orthogonal graph (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947315002716
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:96:y:2016:i:c:p:145-158

DOI: 10.1016/j.csda.2015.11.003

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().