Shamshuritawati  Sharif, Nuraimi  Ruslan, Tareq  A.M. Atiany, 
    Type 1 Error Rate Comparison Between Classical and Modified Box M-Statistic,
    Journal of Engineering and Applied Sciences,
    Volume 13,Issue 5,
    2018,
    Pages 1246-1252,
    ISSN 1816-949x,
    jeasci.2018.1246.1252,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2018.1246.1252)
    Abstract: Classical Box M-statisticis one of Likelihood Ratio Test (LRT) constructed under the multivariate
normality distribution. The performance of classical Box M-statistic by using classical estimators suffers from
masking and swamping effects when the outlier occurs in data set. To alleviate the problem, robust estimators
are recommended. In this study, a robust Box M-statistic based on a S-estimator, M<sub>s</sub> and M-estimator M<sub>M</sub> are
proposed as the alternative to the classical Box M-statistic. Over the simulation study, the performance
comparisonof classical, M<sub>s</sub> and MM-statistics are measured using type 1 error rates. From the results, it showed
that M<sub>s</sub> (Box M-statistic based on S-estimator) has a competitive performance relative to M<sub>M</sub> and the
classicalstatistic. In summary, M<sub>s</sub> can be used for testing the equality of two difference covariance matrices or
more when the data contains outlier.
    Keywords: distribution;multivariate;S-estimator;M-estimator;type 1 error;Covariance matrix