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The Estimation of Ratios From Paired Data

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Empirical Bayes and Likelihood Inference

Part of the book series: Lecture Notes in Statistics ((LNS,volume 148))

Abstract

Fisher many times expressed the view that in inductive inference comparatively slight differences in the mathematical specification of a problem may have logically important effects on the inferences possible, and that in complicated cases, such effects may be very puzzling. The problem of making inferences about ratios from paired data is examined from this viewpoint. The existence and role of likelihood function is emphasized.

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8 References

  • Barnard, G.A. (1994). Pivotal inference illustrated on the darwin maize data. In A. Smith and P. Freeman (Eds.), Aspects of Uncertainty. New York: Wiley.

    Google Scholar 

  • Barnard, G.A. and D.A. Sprott (1983). The generalised problem of the Nile: Robust confidence sets for parametric functions. Ann. Statist. 11, 104–113.

    Article  MathSciNet  MATH  Google Scholar 

  • Chamberlin, S.R. and D.A. Sprott (1987). Some logical aspects of the linear functional relationship. Statist. Papers 28, 291–299.

    Google Scholar 

  • Chamberlin, S.R. and D.A. Sprott (1989). Linear systems of pivotais and associated pivotal likelihoods with applications. Biometrika 76, 685–691.

    Article  MathSciNet  MATH  Google Scholar 

  • Cohen, J.E., P. D’Eustachio, and G.M. Edelman (1977). The specific antigen-binding cell populations of individual fetal mouse spleens: repertoire composition, size and genetic control. J. Exper. Med. 146, 394–411.

    Article  Google Scholar 

  • Creasy, M.A. (1954). Limits for the ratio of means (with discussion). J. Roy. Statist. Soc. Ser. B 16, 186–194.

    MathSciNet  MATH  Google Scholar 

  • Fieller, E.C. (1940). The biological standardization of insulin. J. Roy. Statist. Soc. Suppl. 7.

    Google Scholar 

  • Fieller, E.C. (1954). Some problems in interval estimation (with discussion). J. Roy. Statist. Soc. Ser. B 16, 175–185.

    MathSciNet  MATH  Google Scholar 

  • Fisher, R.A. (1934). Two new properties of mathematical likelihood. Proc. Roy. Statist. Soc. Ser. A 144, 285–307.

    Article  Google Scholar 

  • Fisher, R.A. (1954). Contribution to the symposium on interval estimation. J. Roy. Statist. Soc. Ser. B 16, 212–213.

    Google Scholar 

  • Fisher, R.A. (1991c). Statistical Methods for Research Workers (14th ed.). Statistical Methods, Experimental Design, and Scientific Inference. Oxford: Oxford University Press.

    Google Scholar 

  • Fisher, R.A. (1991a). The Design of Experiments (8th ed.). Statistical Methods, Experimental Design, and Scientific Inference. Oxford: Oxford University Press.

    Google Scholar 

  • Fisher, R.A. (1991b). Statistical Methods and Scientific Inference (3rd ed.). Statistical Methods, Experimental Design, and Scientific Inference. Oxford: Oxford University Press.

    Google Scholar 

  • Fuller, W.A. (1987). Measurement Error Models. New York: John Wiley and Sons.

    Book  MATH  Google Scholar 

  • Kalbfleisch, J.D. and D.A. Sprott (1970). Application of likelihood methods to models involving large numbers of parameters (with discussion). J. Roy. Statist. Soc. Ser. B 32, 175–208.

    MathSciNet  MATH  Google Scholar 

  • Schneeweiss, H., Sprott, D.A., and R. Viveros (1987). An approximate conditional analysis of the linear functional relationship. Statist. Papers 28, 183–202.

    MATH  Google Scholar 

  • Sprott, D.A. (1978). Robustness and nonparametric procedures are not the only or safe alternatives to normality. Canad. J. Psychology 32, 180–185.

    Article  Google Scholar 

  • Sprott, D.A. (1982). Robustness and maximum likelihood. Communications in Statist. Theory and Method 11, 2513–2529.

    Article  MathSciNet  MATH  Google Scholar 

  • Sprott, D.A. (1990). Inferential estimation, likelihood, and linear pivotais (with discussion). Canad. J. Statist. 18, 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  • Sprott, D.A. and V.T. Farewell (1993). The difference between two normal means. Amer. Statistician 47, 126–128.

    Google Scholar 

  • Viveros, R. and D.A. Sprott (1987). Allowance for skewness in maximum likelihood estimation with application to the location-scale model. Canad. J. Statist. 15, 349–361.

    Article  MathSciNet  MATH  Google Scholar 

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© 2001 Springer Science+Business Media New York

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Sprott, D.A. (2001). The Estimation of Ratios From Paired Data. In: Ahmed, S.E., Reid, N. (eds) Empirical Bayes and Likelihood Inference. Lecture Notes in Statistics, vol 148. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0141-7_10

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  • DOI: https://doi.org/10.1007/978-1-4613-0141-7_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-95018-1

  • Online ISBN: 978-1-4613-0141-7

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