Erich Lehmann’s Contributions to Orderings of Probability Distributions

  • Marco Scarsini
Open Access
Part of the Selected Works in Probability and Statistics book series (SWPS)


The initial contributions to the theory of comparison of experiments appeared in the late forties/early fifities (see, e.g., Bohnenblust, Shapley, and Sherman, 1949; Stein, 1951; Blackwell, 1951, 1953).


Decision Procedure Stochastic Order Monotone Transformation Initial Contribution Monotone Likelihood Ratio 
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  1. Athey, S. and Levin, J. (2001) The Value of Information in Monotone Decision Problems. Working Paper 98-24, MIT.Google Scholar
  2. Bartoszewicz, J. and Benduch, M. (2009) Some properties of the generalized TTT transform. J. Statist. Plann. Inference 139, 2208 2217.MathSciNetGoogle Scholar
  3. Bergemann, D. and Valimaki, J. (2002) Information acquisition and efficient mechanism design. Econometrica 70, 1007-1033.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Bickel, P. J. and Lehmann, E. L. (1979) Descriptive statistics for nonparametric models. IV. Spread. In Contributions to statistics, 33-40. Reidel, Dordrecht.CrossRefGoogle Scholar
  5. Blackwell, D. (1951) Comparison of experiments. In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, 93-102. University of California Press, Berkeley and Los Angeles.Google Scholar
  6. Blackwell, D. (1953) Equivalent comparisons of experiments. Ann. Math. Statistics 24, 265-272.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Bohnenblust, H. F., Shapley, L. S., and Sherman, S. (1949) Reconnaissance in game theory. Technical Report RM 208, RAND Corporation, Santa Monica, CA. URL
  8. Jewitt, I. (2007) Information order in decision and agency problems. Mimeo, Nuffield College.Google Scholar
  9. Kamae, T., Krengel, U., and O’Brien, G. L. (1977) Stochastic inequalities on partially ordered spaces. Ann. Probability 5, 899-912.MathSciNetzbMATHCrossRefGoogle Scholar
  10. Karlin, S. and Rinott, Y. (1980) Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions. J. Multivariate Anal. 10, 467-498.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Karlin, S. and Rubin, H. (1956a) Distributions possessing a monotone likelihood ratio. J. Amer. Statist. Assoc. 51, 637-643.MathSciNetzbMATHCrossRefGoogle Scholar
  12. Karlin, S. and Rubin, H. (1956b) The theory of decision procedures for distributions with monotone likelihood ratio. Ann. Math. Statist. 27, 272-299.MathSciNetzbMATHCrossRefGoogle Scholar
  13. Le Cam, L. (1996) Comparison of experiments—a short review. In Statistics, probability and game theory, volume 30 of IMS Lecture Notes Monogr. Ser., 127-138. Inst. Math. Statist., Hayward, CA. URL Scholar
  14. Lehmann, E. L. (1952) Testing multiparameter hypotheses. Ann. Math. Statistics 23, 541 552.Google Scholar
  15. Lehmann, E. L. (1955) Ordered families of distributions. Ann. Math. Statist. 26, 399-419.MathSciNetzbMATHCrossRefGoogle Scholar
  16. Lehmann, E. L. (1988) Comparing location experiments. Ann. Statist. 16, 521-533.MathSciNetzbMATHCrossRefGoogle Scholar
  17. Lehmann, E. L. and ROJO, J. (1992) Invariant directional orderings. Ann. Statist. 20, 2100-2110.MathSciNetzbMATHCrossRefGoogle Scholar
  18. Levin, J. (2001) Information and the market for lemons. Rand J. Econom. 32, 657-666.CrossRefGoogle Scholar
  19. Muller, A. and Stoyan, D. (2002) Comparison methods for stochastic models and risks. Wiley Series in Probability and Statistics. John Wiley & Sons Ltd., Chichester.Google Scholar
  20. PERSICO, N. (2000) Information acquisition in auctions. Econometrica 68, 135 148.Google Scholar
  21. Quah, J. K.-H. and Strulovici, B. (2009) Comparative statics, informativeness, and the interval dominance order. Econometrica 77, 1949 1992.MathSciNetGoogle Scholar
  22. Shared, M. and Shanthikumar, J. G. (2007) Stochastic orders. Springer Series in Statistics. Springer, New York. URL  10.1007/978-0-387-34675-5.
  23. Stein, C. (1951) Notes on a Seminar on Theoretical Statistics. I. Comparison of experiments. University of Chicago.Google Scholar
  24. Strassen, V. (1965) The existence of probability measures with given marginals. Ann. Math. Statist. 36, 423-439.MathSciNetzbMATHCrossRefGoogle Scholar
  25. Torgersen, E. (1991) Comparison of statistical experiments, volume 36 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge.Google Scholar
  26. Whitt, W. (1982) Multivariate monotone likelihood ratio and uniform conditional stochastic order. J. Appl. Probab. 19, 695-701.MathSciNetzbMATHCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Dipartimento di Economia e FinanzaLUISSRomaItaly

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