ABSTRACT
This chapter explores the multivariate distribution of Xi j in terms of these covariates. Most simply, these covariates often indicate group membership. Standard parametric analyses presuppose distributions of data well-enough behaved that location can be well-estimated using a sample mean. The chapter considers testing the null hypothesis that the vector µ of expectations takes on some value specified in advance; without loss of generality, take this value to be 0. Consider a null hypothesis stating that the marginal median vector takes on a value specified in advance; without loss of generality, take this to be zero. In the multivariate Gaussian context, the statistic represents the combination of separate location test statistics for the various components of the random vectors, and its distribution depends on multivariate normality of the underlying observations.
