Inference after truncated one-sided sequential test

ABSTRACT

Assume i.i.d. random variables {X₁, …, X_n, …} follow the standard exponential family {dF_θ(x) = exp(θx − c(θ))dF₀(x)}. For the one-sided hypothesis test H₀: θ = θ₀ < 0 and H_a: 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).

Keywords:

• Corrected pivot
• Exponential family
• Strong renewal theorem
• Truncated sequential test

Mathematics Subject Classification:

• Primary 60L10
• Secondary 60L12
• 60L15

Acknowledgment

I am grateful to the Editor’s suggestions and the comments from a reviewer which led to significant improvement of presentation.