Conservative Multiple Use Con dence Regions inMultivariate

be independent multivariate observations , where the x i 's are known vectors, B; and are unknown, being a positive deenite matrix. The calibration problem deals with statistical inference concerning and the problem that we have addressed is the construction of conndence regions. When the same set of y i 's are used to construct conndence regions for a sequence of possibly diierent parameter vectors , corresponding to a sequence of independent y's, we have what are called multiple use conndence regions. Two coverage probabilities, say 1 ? and 1 ?; are used to characterize such conndence regions. The proportion of conndence regions that will include the corresponding true-values, given that the same y i 's are used in their construction, is to be at least 1 ?. The probability that the y i 's will guarantee such a 100(1 ?)% coverage is to be at least 1 ?. In this article, we construct a conservative multiple use conndence region for. The situation where is a possibly non-linear function, say h(); of fewer unknown parameters denoted by the vector , is also considered. The problem addressed in this context is the construction of a multiple use conndence region for. The numerical computations required for the practical implementation of our conndence region are explained in detail and illustrated using an example. For the multivariate models considered, ours is the rst solution to the problem of constructing multiple use conndence regions.