In this paper Chow and Robbins' (1965) sequential theory has been extended to construct a confidence region with prescribed maximum width and prescribed coverage probability for the linear regression parameters under weaker conditions than Srivastava (1967), Albert (1966), and Gleser (1965). An extension to multivariate case has also been carried out.
M. S. Srivastava. "On Fixed-Width Confidence Bounds for Regression Parameters." Ann. Math. Statist. 42 (4) 1403 - 1411, August, 1971. https://doi.org/10.1214/aoms/1177693251