mvnorm.test {energy} | R Documentation |
E-statistic (Energy) Test of Multivariate Normality
Description
Performs the E-statistic (energy) test of multivariate or univariate normality.
Usage
mvnorm.test(x, R)
mvnorm.etest(x, R)
mvnorm.e(x)
Arguments
x |
data matrix of multivariate sample, or univariate data vector |
R |
number of bootstrap replicates |
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, mvnorm.e
returns the univariate statistic
normal.e(x)
.
If the data contains missing values or the sample covariance matrix is
singular, mvnorm.e
returns NA.
The -test of multivariate normality was proposed
and implemented by Szekely and Rizzo (2005). The test statistic for
d-variate normality is given by
where is the standardized sample,
are iid standard d-variate normal, and
denotes Euclidean norm.
The -test of multivariate (univariate) normality
is implemented by parametric bootstrap with
R
replicates.
Value
The value of the -statistic for multivariate
normality is returned by
mvnorm.e
.
mvnorm.test
returns a list with class htest
containing
method |
description of test |
statistic |
observed value of the test statistic |
p.value |
approximate p-value of the test |
data.name |
description of data |
mvnorm.etest
is replaced by mvnorm.test
.
Note
If the data is univariate, the test statistic is formally
the same as the multivariate case, but a more efficient computational
formula is applied in normal.e
.
normal.test
also provides an optional method for the
test based on the asymptotic sampling distribution of the test
statistic.
Author(s)
Maria L. Rizzo mrizzo@bgsu.edu and Gabor J. Szekely
References
Szekely, G. J. and Rizzo, M. L. (2005) A New Test for Multivariate Normality, Journal of Multivariate Analysis, 93/1, 58-80, doi:10.1016/j.jmva.2003.12.002.
Mori, T. F., Szekely, G. J. and Rizzo, M. L. "On energy tests of normality." Journal of Statistical Planning and Inference 213 (2021): 1-15.
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.test
for the energy test of univariate
normality and normal.e
for the statistic.
Examples
## compute normality test statistic for iris Setosa data
data(iris)
mvnorm.e(iris[1:50, 1:4])
## test if the iris Setosa data has multivariate normal distribution
mvnorm.test(iris[1:50,1:4], R = 199)