Suppose we have k independent p-variate normal populations having unknown mean vectors µi and dispersion matrices of the form
is unknown and Hi is a known p x p positive definite matrix, i = 1, 2, ... k. The investigators in these k populations may possibly have implemented different sequential or multistage sampling methodologies to estimate the mean vectors individually, having certain notions of “fixed-precision” tied with their individual problems of statistical inference. In this paper, we examine how such already available sample resources obtained from independent, but comparable studies can be fruitfully combined in order to provide a “fixed-size” confidence region for a linear combination of the k mean vectors. We discuss appropriate asymptotic second-order characteristics for the coverage probability under a fairly broad set of assumptions on the stopping variables. An example has been included involving purely sequential, accelerated sequential and three-stage sampling techniques.
