Wald type tests with the wrong dispersion matrix

Abstract

A Wald type test with the wrong dispersion matrix is used when the dispersion matrix is not a consistent estimator of the asymptotic covariance matrix of the test statistic. One class of such tests occurs when there are p groups and it is assumed that the population covariance matrices from the p groups are equal, but the common covariance matrix assumption does not hold. The pooled t test, one-way ANOVA F test, and one-way MANOVA F test are examples of this class. Another class of such tests is used for weighted least squares. Two bootstrap confidence regions are modified to obtain large sample Wald type tests with the wrong dispersion matrix.

Keywords:

• Bootstrap
• confidence region
• MANOVA
• weighted least squares

Mathematics Subject Classification:

• Primary 62H15
• Secondary 62J10

Acknowledgments

The authors thank the referees for their work.