Inference after truncated one-sided sequential test

Abstract

ABSTRACTAssume i.i.d. random variables {X1, …, Xn, …} follow the standard exponential family {dFθ(x) = exp(θx − c(θ))dF0(x)}. For the one-sided hypothesis test H0: θ = θ0 < 0 and Ha: θ ⩾ θ1 > 0 where c(θ0) = c(θ1), the truncated sequential probability ratio test stops at min (τ, T) where , and H0 is rejected if τ < T. Inference problems based on asymptotic pivots are considered given τ < T by assuming T/b → finite constant larger than 1/c′(θ1).