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Assessment of Multinormality and the Robustness of Hotelling's T 2 . Test
Author(s) -
Mardia K. V.
Publication year - 1975
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2346563
Subject(s) - robustness (evolution) , robustness testing , test (biology) , econometrics , computer science , mathematics , statistics , artificial intelligence , chemistry , geology , biochemistry , gene , fuzzy logic , paleontology
Summary Various techniques of assessing multinormality have appeared within the last few years. Significant developments in this area have included techniques based on the Mahalanobis “angles” and distances. A test of multinormality based on some measures of multivariate skewness and kurtosis has also been proposed by Mardia (1970a). We show the interconnections between these measures by expressing them in terms of the Mahalanobis “angles” and distances. Some additional critical values of the test are also computed. We show how these measures provide a means of interpreting various Monte Carlo studies for the effect of nonnormality on Hotelling's T 2 . The above material is used in examining certain outstanding problems in a numerical example.