Shamshuritawati  Sharif, Nuraimi  Ruslan, Tareq A.M.  Atiany, 
    A Modification of the Box M Statistics Using S Estimator,
    Journal of Engineering and Applied Sciences,
    Volume 13,Issue 10,
    2018,
    Pages 3534-3540,
    ISSN 1816-949x,
    jeasci.2018.3534.3540,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2018.3534.3540)
    Abstract: Box M statistic constructed under the multivariate normality distribution and is one of Llikelihood
Ratio Test (LRT). The performance of traditional Box M statistic by utilizing classical estimators suffers from
masking and swamping effects when there is outlier in data set. To ease the problem, robust estimators are
suggested. A robust Box M statistic based on a S estimator, M<sub>s</sub> suggested as the alternative to the classical 
Box M<sub>s</sub> statistic. From the simulation study, the performance comparison of classical and M statistics are 
measured using power of test. From the results, it displayed that M<sub>s</sub> has a competitive performance relative to 
the classical statistic. As a conclusion, M<sub>s</sub> can be used for testing the equality of two difference covariance 
matrices or more when the data contains outlier.
    Keywords: Covariance matrix;S estimator;power of test;difference;covariance;matrices