Bias reduction for the ratio of means

References

• Chakravarti , I. M. 1971 . Confidence set for the ratio of means of two normal distributions when the ratio of variances is unknown . Biometrische Zeitschrift , 13 : 89 – 94 .
   Google Scholar
• Sevin , A. D. 1978 . Small sample estimation and testing procedures for ratios of means of independent, normally distributed random-variables . Biometrics , 34 : 166 – 166 .
   Google Scholar
• Knapp , R. G. , Gross , A. J. and Cantor , A. B. 1985 . Estimators of the ratio of means of paired survival-data . Biometrics , 41 : 333 – 333 .
   Google Scholar
• Chow , S. C. and Shao , J. 1990 . An alternative approach for the assessment of bioequivalence between 2 formulations of a drug . Biom. J. , 32 : 969 – 976 .
   Web of Science ®Google Scholar
• Hoenig , J. M. , Jones , C. M. , Pollock , K. H. , Robson , D. S. and Wade , D. L. 1997 . Calculation of catch rate and total catch in roving surveys of anglers . Biometrics , 53 : 306 – 317 .
   Web of Science ®Google Scholar
• Hauschke , D. , Kieser , M. and Hothorn , L. A. 1999 . Proof of safety in toxicology based on the ratio of two means for normally distributed data . Biom. J. , 41 : 295 – 304 .
   Web of Science ®Google Scholar
• Mendoza , M. and Gutierrez-Pena , E. 1999 . Bayesian inference for the ratio of the means of two normal populations with unequal variances . Biom. J. , 41 : 133 – 147 .
   Google Scholar
• Wu , J. R. , Jiang , G. Y. , Wong , A. C.M. and Sun , X. 2002 . Likelihood analysis for the ratio of means of two independent log-normal distributions . Biometrics , 58 : 463 – 469 .
   PubMed Web of Science ®Google Scholar
• Li , S. Y. and Zhang , B. X. 2003 . Maximum likelihood estimation of ratios of means and standard deviations from normal populations under semi-order restriction . J. Biomath. , 18 : 257 – 261 .
   Google Scholar
• Diaz-Frances , E. and Sprott , D. A. 2004 . Inference for the ratio of two normal means with unspecified variances . Biom. J. , 46 : 83 – 89 .
   Web of Science ®Google Scholar
• Gregoire , T. G. and Salas , C. 2009 . Ratio estimation with measurement error in the auxiliary variate . Biometrics , 65 : 590 – 598 .
   PubMed Web of Science ®Google Scholar
• Kotz , S. and Johnson , N. L. 1986 . Encyclopedia of Statistical Sciences , Vol. 7 , New York : Wiley .
   Google Scholar
• Fieller , E. C. 1954 . Some problems in interval estimation . J. R. Stat. Soc. B , 16 : 175 – 185 .
   Google Scholar
• Bennett , B. M. 1963 . On combining estimates of a ratio of means . J. R. Stat. Soc. B , 25 : 201 – 205 .
   Google Scholar
• Steffens , F. E. 1971 . On confidence sets for the ratio of two normal means . South African Statist. J. , 5 : 105 – 113 .
   Google Scholar
• James , A. T. , Wilkinson , G. N. and Venables , W. N. 1974 . Interval estimates for a ratio of means . Sankhyā A , 36 : 177 – 183 .
   Google Scholar
• Tsao , C. A. and Hwang , J. T. 1999 . Generalized Bayes confidence estimators for Fieller's confidence sets . Statist. Sinica , 9 : 795 – 810 .
   Google Scholar
• Lee , J. C. and Lin , S. H. 2004 . Generalized confidence intervals for the ratio of means of two normal populations . J. Statist. Plann. Inference , 123 : 49 – 60 .
   Web of Science ®Google Scholar
• Kim , H. J. 2005 . Bayesian analysis for a power of the ratio of two normal means . Far East J. Theor. Stat. , 15 : 143 – 156 .
   Google Scholar
• Mendoza , M. 2005 . Inferences on the ratio of normal means and other related problems . Estadistica , 57 : 168 – 169 .
   Google Scholar
• Dilba , G. , Bretz , F. and Guiard , V. 2006 . Simultaneous confidence sets and confidence intervals for multiple ratios . J. Statist. Plann. Inference , 136 : 2640 – 2658 .
   Web of Science ®Google Scholar
• Shi , H. F. , Li , S. Y. and Ji , Y. G. 2008 . Maximum likelihood estimation of ratios of means and standard deviations from normal populations with different sample numbers under semi-order restriction . J. Math. Res. Exposition , 28 : 1031 – 1036 .
   Google Scholar
• Withers , C. S. 1989 . Accurate confidence intervals when nuisance parameters are present . Comm. Statist. Theory Methods , 18 : 4229 – 4259 .
   Web of Science ®Google Scholar
• Bose , P. 1942 . On the exact distribution of the ratio of two means belonging to samples drawn from a given correlated bivariate normal population . Bull. Calcutta Math. Soc. , 34 : 139 – 141 .
   Google Scholar
• Roy , S. N. and Potthoff , R. F. 1958 . Confidence bounds on vector analogues of the ‘ratio of means’ and the ‘ratio of variances’ for two correlated normal variates and some associated tests . Ann. Math. Statist. , 29 : 829 – 841 .
   Google Scholar
• Malley , J. D. 1982 . Simultaneous confidence intervals for ratios of normal means . J. Amer. Statist. Assoc. , 77 : 170 – 176 .
   Google Scholar
• Hannig , J. 2006 . Asymptotic bounds for coverage probabilities for a class of confidence intervals for ratio of means in a bivariate normal distribution . J. Probab. Statist. Sci. , 4 : 41 – 49 .
   Google Scholar
• Cornish , E. A. and Fisher , R. A. 1937 . “ Moments and cumulants in the specification of distributions ” . Vol. 5 , 307 – 322 . Revue de l'Institut Internat de Statistics . (reproduced in The Collected Papers of R. A. Fisher, volume 4)
   Google Scholar
• Fisher , R. A. and Cornish , E. A. 1960 . The percentile points of distributions having known cumulants . Technometrics , 2 : 209 – 225 .
   Google Scholar
• Withers , C. S. 1991 . Tests and confidence intervals for the shape parameter of a gamma distribution . Comm. Statist. Theory Methods , 20 : 2663 – 2685 .
   Web of Science ®Google Scholar
• Fisher , R. A. 1939 . The comparison of samples with possibly unequal variances . Ann. Eugenics , 9 : 174 – 180 .
   Google Scholar
• Welch , B. L. 1947 . The generalisation of ‘Student's’ problem when several different population variances are involved . Biometrika , 34 : 28 – 35 .
   PubMed Web of Science ®Google Scholar
• Withers , C. S. 1988 . Nonparametric confidence intervals for functions of several distributions . Ann. Inst. Statist. Math. , 40 : 727 – 746 .
   Web of Science ®Google Scholar
• Withers , C. S. 1984 . Asymptotic expansions for distributions and quantiles with power series cumulants . J. R. Stat. Soc. B , 46 : 389 – 396 .
   Google Scholar
• Withers , C. S. 2000 . A simple expression for the multivariate Hermite polynomial . Statist. Probab. Lett. , 47 : 165 – 169 .
   Web of Science ®Google Scholar
• Withers , C. S. 1982 . The distribution and quantiles of a function of parameter estimates . Ann. Inst. Statist. Math. A , 34 : 55 – 68 .
   Web of Science ®Google Scholar