Filipe J. Marques

Instructions for the use of the of the codes of the near-exact distributions for the
likelihood ratio test statistic used to test the sphericity structure of a covariance
matrix.

The computational implementation was made using the software Mathematica. The computational modules described incorporate the results in: Marques, F.J. and Coelho, C.A. (2008). Near-exact distributions for the sphericity likelihood ratio test statistic. Journal of Statistical Planning and Inference, 138, 726-741.

The base modules are the modules available in the web-page:
https://sites.google.com/site/nearexactdistributions/

Please see the detailed instructions HERE

The module to compute the near-exact density and cumulative distribution functions for the negative logarithm of the likelihood ratio test statistic W = −logΛ used to test the sphericity structure of a given covariance matrix are denoted, respectively, by PDFsphericity[p_,n_,x_,dist_:1] presented in Figure 3 and CDFsphericity[p_,n_,x_,dist_:1] in Figure 4.

These modules may be found HERE.

The 4 arguments of the modules are:
p - number of variables;
n=N-1, where N is the sample size;
x - the running value
dist - indicates which near-exact should be computed
(i) value 1 for the single GNIG distribution;
(ii) value 2 for the mixture of 2 GNIG distributions;
(iii) value 3 for the mixture of 3 GNIG distributions;
(iv) in the absence of specification of this argument the module gives it the default value
of 1.