statsmodels.stats.multivariate.test_cov_spherical¶

statsmodels.stats.multivariate.test_cov_spherical(cov, nobs)[source]¶

One sample hypothesis test that covariance matrix is spherical

The Null and alternative hypotheses are

\[\begin{split}H0 &: \Sigma = \sigma I \\ H1 &: \Sigma \neq \sigma I\end{split}\]

where \(\sigma_i\) is the common variance with unspecified value.

Parameters:¶

cov : array_like¶

Covariance matrix of the data, estimated with denominator (N - 1), i.e. ddof=1.

nobs : int¶

number of observations used in the estimation of the covariance

Returns:¶

res – results with statistic, pvalue and other attributes like df

Return type:¶

instance of HolderTuple

References

Bartlett, M. S. 1954. “A Note on the Multiplying Factors for Various Χ2 Approximations.” Journal of the Royal Statistical Society. Series B (Methodological) 16 (2): 296–98.

Rencher, Alvin C., and William F. Christensen. 2012. Methods of Multivariate Analysis: Rencher/Methods. Wiley Series in Probability and Statistics. Hoboken, NJ, USA: John Wiley & Sons, Inc. https://doi.org/10.1002/9781118391686.

StataCorp, L. P. Stata Multivariate Statistics: Reference Manual. Stata Press Publication.