On Fixed-Width Confidence Bounds for Regression Parameters and Mean Vector

Summary In this paper Chow and Robbins's (1965) sequential theory has been extended to construct a confidence region with prescribed maximum width and prescribed coverage probability for (i) the linear regression parameters, and (ii) the mean vector of a multivariate population. Except for the finiteness of the unknown variance and covariances in the respective two cases, no assumption regarding the form of their distribution functions is made. This result was announced in Srivastava (1966a). For some related results, refer to Gleser (1965), Srivastava (1966b) and Starr (1966).