A monotonicity property of the power function of multivariate tests. (English) Zbl 0970.62038
Summary: Let , where the are independent observations from a 2-dimensional normal distribution, and let be a diagonal matrix of the form , where and is the identity matrix. It is shown that the density of the vector of characteristic roots of can be written as , where satisfies the FKG condition on . This implies that the power function of tests with monotone acceptance region in and , i.e. a region of the form , where is nondecreasing in each argument, is nondecreasing in . It is also shown that the density of does not allow a decomposition , with satisfying the FKG condition, if and , implying that this approach to proving monotonicity of the power function fails in general.
|62H15||Multivariate hypothesis testing|
|62H10||Multivariate distributions of statistics|