Sequential confidence sets with guaranteed coverage probability and beta-protection

A general procedure for constructing sequential confidence sets for a vector valued parameter, having a coverage probability at least 1-[alpha] and probability of covering a certain set of false values at most [beta], is developed. The limiting values of the error probabilities are found as the parameter approaches the boundary points. Applications are made to the problem of confidence sets for the mean vector and the covariance matrix of a multivariate normal, and to the multiple regression model.