TY  - JOUR
T1  - Type 1 Error Rate Comparison Between Classical and Modified Box M-Statistic
AU - Sharif, Shamshuritawati AU - Ruslan, Nuraimi AU - A.M. Atiany, Tareq 
JO  - Journal of Engineering and Applied Sciences
VL  - 13
IS  - 5
SP  - 1246
EP  - 1252
PY  - 2018
DA  - 2001/08/19
SN  - 1816-949x
DO  - jeasci.2018.1246.1252
UR  - https://makhillpublications.co/view-article.php?doi=jeasci.2018.1246.1252
KW  - distribution
KW  -multivariate
KW  -S-estimator
KW  -M-estimator
KW  -type 1 error
KW  -Covariance matrix
AB  - 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.
ER  -