Two Non-Regular Extensions of Large Deviation Bound

References

• Akahira , M. ( 1996 ). Loss of information of a statistic for a family of non-regular distributions . Ann. Inst. Stat. Math. 48 ( 2 ): 349 – 364 .
   Google Scholar
• Akahira , M. , Takeuchi , K. ( 1995 ). Non-Regular Statistical Estimation . Lecture Notes in Statistics, No. 107. Springer .
   Google Scholar
• Bahadur , R. R. ( 1960 ). Asymptotic efficiency of tests and estimates . Sankhyā 22 : 229 – 252 .
   Google Scholar
• Bahadur , R. R. ( 1967 ). Rates of convergence of estimates and test statistics . Ann. Math. Stat. 38 : 303 – 324 .
   Google Scholar
• Bahadur , R. R. ( 1971 ). Some Limit Theorems in Statistics . Regional Conference Series in Applied Mathematics, No. 4. SIAM .
   Google Scholar
• Cheng , R. C. H. , Traylor , L. ( 1995 ). Non-regular maximum likelihood problem . J. Roy. Stat. Soc. B 57 : 3 – 44 .
   Google Scholar
• Chernoff , H. ( 1952 ). A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations . Ann. Math. Stat. 23 : 493 – 507 .
   Google Scholar
• Fu , J. C. ( 1973 ). On a theorem of Bahadur on the rate of convergence of point estimator . Ann. Stat. 1 : 745 – 749 .
   Web of Science ®Google Scholar
• Fu , J. C. ( 1985 ). On exponential rates of likelihood ratio estimators for location parameters . Stat. Probab. Lett. 3 : 101 – 105 .
   Google Scholar
• Hayashi , M. ( 2002a ). Limiting behavior of relative Rényi entropy in a non-regular location shift family . Ann. ISM. Available at: http://arxiv.org/abs/math/0212077
   Google Scholar
• Hayashi , M. ( 2002b ). Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation . J. Phys. Math. Gen. 35 : 7689 – 7727 .
   Google Scholar
• Hoeffding , W. ( 1965 ). Asymptotically optimal tests for multinomial distributions . Ann. Math. Stat. 36 : 369 – 400 .
   Google Scholar
• Huber , P. J. ( 1968 ). Robust confidence limits . Zeitschnift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 10 : 269 – 278 .
   Web of Science ®Google Scholar
• Ibragimov , I. A. , Has'minskii , R. Z. (1981). Statistical Estimation . Springer.
   Google Scholar
• Nagaoka , H. ( 2005 ). On the relation between Kullback divergence and Fisher information—from classical systems to quantum systems . In: Hayashi , M. , ed. Asymptotic Theory of Quantum Statistical Inference . Singapore : World Scientific , p. 399 .
   Google Scholar
• Nagaoka , H. ( 1994 ). Two quantum analogues of the large deviation Cramér–Rao inequality . Proc. 1994 IEEE International Symposium on Information Theory. p. 118 .
   Google Scholar
• Sievers , G. L. ( 1978 ). Estimates of location: a large deviation comparison . Ann. Stat. 6 : 610 – 618 .
   Google Scholar
• Smith , R. ( 1985 ). Maximum likelihood estimation in a class of nonregular cases . Biometrika 72 : 67 – 90 .
   Web of Science ®Google Scholar