Bootstrapping analogs of the two-sample hotelling’s T² test

ABSTRACT

Suppose there are two independent random samples from two populations or groups. A common multivariate two-sample test of hypotheses is versus where is a population location measure of the ith population for i = 1, 2. The two-sample Hotelling’s T² test is the classical method, and is a special case of the one way MANOVA model if the two populations are assumed to have the same population covariance matrix. This paper suggests using a recent bootstrap technique to develop analogs of Hotelling’s T² test. The new tests can have considerable outlier resistance, and the tests do not need the population covariance matrices to be equal.

KEYWORDS:

• Behrens–Fisher problem
• bootstrap
• prediction region
• coordinatewise median
• RMVN estimator.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H15
• Secondary 62G09

Acknowledgments

The authors thank Dr Olive and a referee for comments that improved this paper.