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 Rizzo rizzo@math.ohiou.edu

References

Szekely, G. J. and Rizzo, M. L. (2004) A New Test for Multivariate Normality, Journal of Multivariate Analysis, to appear.

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

normal.e

Examples

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

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