On the robustness of hotelling's T2-test anb distribution of linear and quadratic forms III sampling from a mixture of two mult11ariate normal populations
- 1 January 1982
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 11 (1) , 81-107
- https://doi.org/10.1080/03610928208828219
Abstract
In this paper, the joint distribution of (a) a linear and-a quadratic form, and (b) two quadratic forms are obtained when the sample is taken from a mixture of two p-co»ponent multivariate normal distributions with mean JJ. and JJ« respectively and common covarlaece matrix Z # Also the distribution of Hotelling's t2-statistic is obtained when irji- + (1-ir)^ - j) t where w f O^i^l f Is the mixing proportion (contamination, 1-w). Actual values of a (level of significance) when nominal level a Is 0»05 are computed for some particolar combination of parameters* These results show that the si2e of the test can differ greatly even for a contan-ination as small as 0,05 if the Mahalanobis (square) distance Is large and/or the sample size Is largeKeywords
This publication has 3 references indexed in Scilit:
- One-Sample $t$-Test When Sampling from a Mixture of Normal DistributionsThe Annals of Statistics, 1977
- On the Robustness of Some Tests of Significance in Sampling from a Compound Normal PopulationJournal of the American Statistical Association, 1975
- Distribution of the Means Divided By the Standard Deviations of Samples From Non-Homogeneous PopulationsThe Annals of Mathematical Statistics, 1932