# 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.

*This paper has been withdrawn.*

Wald Type Tests with the Wrong Dispersion Matrix

Volstorff A

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.