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On the characterizing property of the convex conditional mean function

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  • Lillo, Rosa E.

Abstract

In this note, a conjecture of Nagaraja and Nevzorov (J. Statist. Plann. Inference 63 (1997) 271-284) concerning the characterization of a distribution function by its associated convex conditional mean function (CCMF) is proved. The characterizing property of the CCMF holds without the assumptions considered in the result of the above reference. As a consequence, we derive a result of characterization related to the uniform distribution. Applications to the characterization of a c.d.f. based on properties of certain regression functions associated with the order statistics are discussed.

Suggested Citation

  • Lillo, Rosa E., 2004. "On the characterizing property of the convex conditional mean function," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 19-24, January.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:1:p:19-24
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    References listed on IDEAS

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    1. Arjun Gupta & Jacek Wesolowski, 1997. "Uniform Mixtures Via Posterior Means," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 171-180, March.
    2. Lillo R. E. & Martín M., 1999. "Characterization Of Bayes Estimators Of The Uniform Scale Parameter," Statistics & Risk Modeling, De Gruyter, vol. 17(1), pages 31-48, January.
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