Exponentially Bounded Stopping Times of Invariant SPRT's in General Linear Models: Finite $\operatorname{mgf}$ Case

Abstract

A general theorem which is useful in proving the exponential boundedness of the stopping time of sequential tests for parameters in general linear models is formulated; this theorem is formulated under the assumptions that the squared error has a finite moment-generating function and the sequence of the running averages of the concomitant variables converges. Applications are given.