




Estatistics (energy statistics)
Research and software related to Estatistics
Estatistics (energy statistics) refers to a class of tests and statistics
based on Euclidean distances. Applications include testing
multivariate normality, multivariate distance components and
ksample test for equal distributions, hierarchical clustering by edistances,
multivariate independence tests, distance correlation, goodnessoffit tests.
Gabor J. Szekely, National Science Foundation
Maria L. Rizzo,
Bowling Green State University, email:
R software: Energy statistics are implemented in the contributed
package
energy for R.
References
 G. J. Szekely and M. L. Rizzo (2013).
Energy statistics: statistics based on distances.
Journal of Statistical Planning and Inference
Volume 143, Issue 8, August 2013, pp. 12491272.
DOI
 G. J. Szekely and M. L. Rizzo (2013).
The distance correlation ttest of independence in high dimension.
Journal of Multivariate Analysis, Volume 117, pp. 193213.
DOI
 G. J. Szekely and M. L. Rizzo (2012).
On the uniqueness of distance covariance.
Statistics & Probability Letters, Volume 82, Issue 12, 22782282.
DOI
 Maria L. Rizzo and Gabor J. Szekely (2010).
DISCO Analysis: A Nonparametric Extension of Analysis of Variance,
Annals of Applied Statistics Vol. 4, No. 2, 10341055.
Reprint
DOI
 Gabor J. Szekely and Maria L. Rizzo (2009). Brownian Distance
Covariance,
Annals of Applied Statistics,
Vol. 3, No. 4, 12361265.
Reprint
doi:10.1214/09AOAS312
 Gabor J. Szekely and Maria L. Rizzo (2009). Rejoinder: Brownian Distance.
Covariance, Annals of Applied Statistics, Vol. 3, No. 4, 13031308.
Reprint
doi:10.1214/09AOAS312REJ
 Maria. L. Rizzo (2009). New GoodnessofFit Tests for Pareto Distributions,
ASTIN Bulletin: Journal of the International Association of Actuaries,
39/2, 691715. PDF
 G. J. Szekely, M. L. Rizzo, and N. K. Bakirov (2007).
Measuring and Testing Independence by Correlation of Distances, Annals of Statistics,
Vol. 35 No. 6, pp. 27692794.
http://dx.doi.org/10.1214/009053607000000505.
Reprint

Bakirov, N. K., Rizzo, M. L., and Szekely, G. J. (2006).
A Multivariate Nonparametric Test of Independence, Journal of Multivariate Analysis
Volume 97, Issue 8 , September 2006, Pages 17421756
http://dx.doi.org/10.1016/j.jmva.2005.10.005.
 Szekely, G. J. and Rizzo, M. L. (2005) Hierarchical Clustering
via Joint BetweenWithin Distances: Extending Ward's Minimum Variance Method,
Journal of Classification, 22(2) 151183.
http://dx.doi.org/10.1007/s0035700500129.
 Szekely, G. J. and Rizzo, M. L. (2005) A New Test for
Multivariate Normality,
Journal of Multivariate Analysis,
93/1, 5880.
http://dx.doi.org/10.1016/j.jmva.2003.12.002.
Reprint
 Szekely, G. J. and Rizzo, M. L. (2004b) Mean Distance Test of Poisson Distribution,
Statistics and Probability Letters, 67/3, 241247
http://dx.doi.org/10.1016/j.spl.2004.01.005.
 Rizzo, M. L. (2003) Hierarchical Clustering Based on a Generalized
Measure of Homogeneity,
2003 Proceedings of the Joint Statistical Meetings, American Statistical
Association, Section for Physical and Engineering Sciences [CDROM],
Alexandria, VA: American Statistical Association.
 Szekely, G. J. and Rizzo, M. L. (2004) Testing for Equal
Distributions in High Dimension, InterStat, Nov. (5).
Reprint
 M. L. Rizzo (2005) Minimum Energy Clustering
Proceedings of Interface/Classification Society of North America,
Joint Annual Meeting, 2005.
 Rizzo, M. L. (2002a). A Test of Homogeneity for Two Multivariate Populations,
2002 Proceedings of the American Statistical Association, Physical and Engineering
Sciences Section [CDROM], Alexandria, VA: American Statistical Association.
 Rizzo, M. L. (2002b). A New Rotation Invariant GoodnessofFit Test,
Ph.D. dissertation, Bowling Green State University.
Abstract
 Szekely, G. J. (2000) Estatistics: Energy of
Statistical Samples, Bowling Green State University, Department of
Mathematics and Statistics Technical Report No. 0305.
 Szekely, G. J. (1989) Potential and Kinetic Energy in Statistics,
Lecture Notes, Budapest Institute of Technology (Technical University).
R is a free software environment
for statistical computing and graphics, available at the
Comprehensive R
Archive Network (CRAN)..
This software is distributed under
GNU General
Public License Version 2, or later. See
COPYING for the license.
Questions or comments on software: Maria Rizzo, email address above
[go to References]
Current version
energy_1.6.0 released 20130512.
Summary of recent changes in energy package
NEWS
 distance correlation ttest for high dimension implemented (introduced in SR 2013, JMVA)
 In eqdist.e and eqdist.etest, method="disco"
was replaced by two options: "discoB" (between sample
components) and "discoF" (disco F ratio).
 In distance components: Added disco.between and internal functions
that compute the disco betweensample component and
corresponding test.
(DIStance COmponents) function and test added in
energy (version 1.20 27Sept2010)
disco provides a nonparametric approach to analysis
of structured data, using distance components rather than variance components.
The statistic is related to, but not equivalent to, the ksample statistic.
A disco method has been added to the eqdist.etest function and the corresponding
eqdist.e statistic.

distance correlation and distance covariance:
The dcov package is now merged into energy version 1.10
package, available on CRAN 07Apr2008.
MATLAB:
Some functions in energy have been translated to Matlab.
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