TY  - JOUR
T1  - A Modification of the Box M Statistics Using S Estimator
AU - Sharif, Shamshuritawati AU - Ruslan, Nuraimi AU - Atiany, Tareq A.M. 
JO  - Journal of Engineering and Applied Sciences
VL  - 13
IS  - 10
SP  - 3534
EP  - 3540
PY  - 2018
DA  - 2001/08/19
SN  - 1816-949x
DO  - jeasci.2018.3534.3540
UR  - https://makhillpublications.co/view-article.php?doi=jeasci.2018.3534.3540
KW  - Covariance matrix
KW  -S estimator
KW  -power of test
KW  -difference
KW  -covariance
KW  -matrices
AB  - 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.
ER  -