Multivariate generalization of t'- statistic based on the mean square successive difference

The usual t-statistic is not useful if the successive observations have some kind of linear trend. This generally arises in the drug testing experiment and it is clearly pointed out by Shah (1988). He suggests to use t'-statistic which is defined by for testing μ = 0 where , and y1.,…,yk are independent observations from . We generalize this statistic to multivariate situation and define T'-statistic as where .The exact null distribution of T' and an approximate null distribution of T' are obtained. For p = 1, this approximate values are compared.