mvnorm.e {energy}R Documentation

E-statistic (Energy Statistic) for Testing Multivariate Normality

Description

Computes the E-statistic (energy statistic) for testing multivariate or univariate normality when parameters are estimated.

Usage

mvnorm.e(x)

Arguments

x matrix or vector of sample data

Details

If x is a matrix, each row is a multivariate observation. The data will be standardized to zero mean and identity covariance matrix using the sample mean vector and sample covariance matrix. If x is a vector, the univariate statistic normal.e(x) is returned. If the data contains missing values or the sample covariance matrix is singular, NA is returned.

The E-test of multivariate normality was proposed and implemented by Szekely and Rizzo (2004). The test statistic for d-variate normality is given by

E = n((2/n) sum[1:n] E||y_i-Z|| - E||Z-Z'|| - (1/n^2) sum[1:n,1:n] ||y_i-y_j||),

where y_1,...,y_n is the standardized sample, Z, Z' are iid standard d-variate normal, and || || denotes Euclidean norm.

Value

The value of the E-statistic for multivariate (univariate) normality is returned.

Author(s)

Maria L. Rizzo rizzo@math.ohiou.edu and Gabor J. Szekely gabors@bgnet.bgsu.edu

References

Szekely, G. J. and Rizzo, M. L. (2004) A New Test for Multivariate Normality, Journal of Multivariate Analysis, http://dx.doi.org/10.1016/j.jmva.2003.12.002.

Rizzo, M. L. (2002). A New Rotation Invariant Goodness-of-Fit Test, Ph.D. dissertation, Bowling Green State University.

Szekely, G. J. (1989) Potential and Kinetic Energy in Statistics, Lecture Notes, Budapest Institute of Technology (Technical University).

See Also

mvnorm.etest, normal.e

Examples

 
 ## compute multivariate normality test statistic for iris Setosa data
 data(iris)
 mvnorm.e(iris[1:50, 1:4])
 

[Package Contents]