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Marshall lemma in discrete convex estimation

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  • Balabdaoui, Fadoua
  • Durot, Cécile

Abstract

We show that the supremum distance between the cumulative distribution of the convex LSE and an arbitrary distribution function F with a convex pmf on N is at most twice the supremum distance between the empirical distribution function and F.

Suggested Citation

  • Balabdaoui, Fadoua & Durot, Cécile, 2015. "Marshall lemma in discrete convex estimation," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 143-148.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:143-148
    DOI: 10.1016/j.spl.2015.01.016
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    References listed on IDEAS

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    1. Balabdaoui, Fadoua & Rufibach, Kaspar, 2008. "A second Marshall inequality in convex estimation," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 118-126, February.
    2. Durot, Cécile & Huet, Sylvie & Koladjo, François & Robin, Stéphane, 2013. "Least-squares estimation of a convex discrete distribution," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 282-298.
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    Cited by:

    1. Giguelay, J. & Huet, S., 2018. "Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 96-115.

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