Abstract
Assessing the degree to which two probability density functions overlap is an important problem in several applications. Most of the existing proposals to tackle this problem can only deal with univariate distributions. For multivariate problems, existing methods often rely on unrealistic parametric distributional assumptions or are such that the corresponding univariate marginal measures are combined using ad hoc procedures. In this paper, we propose a new empirical measure of the degree of overlap of two multivariate distributions. Our proposal makes no assumptions on the form of the densities and can be efficiently computed even in relatively high-dimensional problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arias-Castro, E., Pelletier, B.: On the consistency of the crossmatch test (2015). arXiv:1509.05790 [math.ST]
Geange, S.W., Pledger, S., Burns, K.C., Shima, J.S.: A unified analysis of niche overlap incorporating data of different types. Methods Ecol. Evol. 2, 175–184 (2011)
Gelman, A., Hill, J.: Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press, Cambridge (2007)
Heller, R., Small, D., Rosenbaum, P.: crossmatch: the cross-match test. R package version 1.3-1 (2012). https://CRAN.R-project.org/package=crossmatch
Meredith, M., Ridout, M.: Overlap: estimates of coefficient of overlapping for animal activity patterns. R package version 0.3.2 (2018). https://CRAN.R-project.org/package=overlap
Pepe, M.S.: The Statistical Evaluation of Medical Tests for Classification and Prediction. University Press, Oxford (2003)
R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2018). https://www.R-project.org/
Ridout, M.S., Linkie, M.: Estimating overlap of daily activity patterns from camera trap data. J. Agric. Biol. Environ. Stat. 14, 322–337 (2009)
Rosenbaum, P.R.: An exact distribution-free test comparing two multivariate distributions based on adjacency. J. R. Stat. Soc. B 67, 515–530 (2005)
Swanson, H.K., Lysy, M., Power, M., Stasko, A.D., Johnson, J.D., Reist, J.D.: A new probabilistic method for quantifying \(n\)-dimensional ecological niches and niche overlap. Ecology 96, 318–324 (2015)
Acknowledgements
The work of the first author was partially supported by the Sistema Nacional de Investigadores, Mexico. The authors are grateful for the comments and suggestions of the editor and two reviewers on an earlier version of the paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Gutiérrez-Peña, E., Walker, S.G. (2019). An Efficient Method to Determine the Degree of Overlap of Two Multivariate Distributions. In: Antoniano-Villalobos, I., Mena, R., Mendoza, M., Naranjo, L., Nieto-Barajas, L. (eds) Selected Contributions on Statistics and Data Science in Latin America. FNE 2018. Springer Proceedings in Mathematics & Statistics, vol 301. Springer, Cham. https://doi.org/10.1007/978-3-030-31551-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-31551-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-31550-4
Online ISBN: 978-3-030-31551-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)