@article{MAKHILLJEAS201813515693,
    title = {Type 1 Error Rate Comparison Between Classical and Modified Box M-Statistic},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {13},
    number = {5},
    pages = {1246-1252},
    year = {2018},
    issn = {1816-949x},
    doi = {jeasci.2018.1246.1252},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2018.1246.1252},
    author = {Shamshuritawati,Nuraimi and},
    keywords = {distribution,multivariate,S-estimator,M-estimator,type 1 error,Covariance matrix},
    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.}
    }