Performs Tests for the structure of covariance matrices.

Ahmad2015(x, Sigma = "identity", ...)

Chen2010(x, Sigma = "identity", ...)

Fisher2012(x, Sigma = "identity", ...)

LedoitWolf2002(x, Sigma = "identity", ...)

Nagao1973(x, Sigma = "identity", ...)

Srivastava2005(x, Sigma = "identity", ...)

Srivastava2011(x, Sigma = "identity", ...)

Arguments

x

data as a list of matrices

Sigma

Population covariance matrix as a matrix

...

other options passed to covTest method

Value

A list with class "htest" containing the following components:

statisticthe value of equality of covariance test statistic
parameterthe degrees of freedom for the chi-squared statistic
p.valuethe p=value for the test
estimatethe estimated covariances if less than 5 dimensions
null.valuethe specified hypothesized value of the covariance difference
alternativea character string describing the alternative hyposthesis
methoda character string indicating what type of equality of covariance test was performed
data.namea character string giving the names of the data

References

Ahmad, M. R. and Rosen, D. von. (2015). Tests for High-Dimensional Covariance Matrices Using the Theory of U-statistics. Journal of Statistical Computation and Simulation, 85(13), 2619-2631. 10.1080/00949655.2014.948441

Chen, S., et al. (2010). Tests for High-Dimensional Covariance Matrices. Journal of the American Statistical Association, 105(490):810-819. 10.1198/jasa.2010.tm09560

Fisher, T. J. (2012). On Testing for an Identity Covariance Matrix when the Dimensionality Equals or Exceeds the Sample Size. Journal of Statistical Planning and Infernece, 142(1), 312-326. 10.1016/j.jspi.2011.07.019

Ledoit, O., and Wolf, M. (2002). Some Hypothesis Tests for the Covariance Matrix When the Dimension Is Large Compared to the Sample Size. The Annals of Statistics, 30(4), 1081-1102. 10.1214/aos/1031689018

Nagao, H. (1973). On Some Test Criteria for Covariance Matrix. The Annals of Statistics, 1(4), 700-709

Srivastava, M. S. (2005). Some Tests Concerning the Covariance Matrix in High Dimensional Data. Journal of the Japan Statistical Society, 35(2), 251-272. 10.14490/jjss.35.251

Srivastava, M. S., Kollo, T., and Rosen, D. von. (2011). Some Tests for the Covariance Matrix with Fewer Observations then the Dimension Under Non-normality. Journal of Multivariate Analysis, 102(6), 1090-1103. 10.1016/j.jmva.2011.03.003

See also

Other Testing for Structure of Covariance Matrices: structureCovariances

Examples

Chen2010(as.matrix(iris[1:50, 1:3]))
#> #> Chen et al. 2010 Test of Covariance Matrix Structure #> #> data: #> Standard Normal = -180.68, Mean = 0, Variance = 1, p-value < 2.2e-16 #> alternative hypothesis: true difference between the Sample Covariance Matrix and the Null Covariance Matrix Structure is not equal to 0 #> sample estimates: #> Sepal.Length Sepal.Width Petal.Length #> Sepal.Length 0.12424898 0.09921633 0.01635510 #> Sepal.Width 0.09921633 0.14368980 0.01169796 #> Petal.Length 0.01635510 0.01169796 0.03015918 #>