A Proof of the Asymptotic Equivalence of Two-Tail Probability Approximations

References

• Fisher , R. A. ( 1935 ). The Design of Experiments . Edinburgh : Oliver and Boyd .
   Google Scholar
• Jensen , J. L. ( 1992 ). The modified signed likelihood statistic and saddlepoint approximations . Biometrika 79 ( 4 ): 693 – 703 .
   Web of Science ®Google Scholar
• Jing , B. , Robinson , J. ( 1994 ). Saddlepoint approximations for marginal and conditional probabilities of transformed variables . Ann. Statist. 22 ( 3 ): 1115 – 1132 .
   Web of Science ®Google Scholar
• Kolassa , J. E. ( 1997 ). Series Approximation Methods in Statistics. , 2nd ed. New York : Springer-Verlag .
   Google Scholar
• Kolassa , J. E. , Robinson , J. ( 2004 ). Conditional saddlepoint approximations for non-continuous and non-lattice distributions . Rutgers University Department of Statistics Technical Report 2004-001 .
   Google Scholar
• Lugannani , R. , Rice , S. ( 1980 ). Saddle point approximation for the distribution of the sum of independent random variables . Adv. App. Probab. 12 ( 2 ): 475 – 490 .
   Web of Science ®Google Scholar
• Robinson , J. ( 1982 ). Saddlepoint approximations for permutation tests and confidence intervals . J. Roy. Statist. Soc. Ser. B 44 ( 1 ): 91 – 101 .
   Google Scholar