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A second Marshall inequality in convex estimation

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  • Balabdaoui, Fadoua
  • Rufibach, Kaspar

Abstract

We prove a second Marshall inequality for adaptive convex density estimation via least squares. The result completes the first inequality proved recently by Dümbgen et al. [2007. Marshall's lemma for convex density estimation. IMS Lecture Notes--Monograph Series, submitted for publication. Preprint available at ], and is very similar to the original Marshall inequality in monotone estimation.

Suggested Citation

  • Balabdaoui, Fadoua & Rufibach, Kaspar, 2008. "A second Marshall inequality in convex estimation," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 118-126, February.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:2:p:118-126
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    References listed on IDEAS

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    1. Jayanta Kumar Pal & Michael Woodroofe, 2006. "On the Distance Between Cumulative Sum Diagram and Its Greatest Convex Minorant for Unequally Spaced Design Points," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 279-291, June.
    2. Gneiting, Tilmann, 1999. "Radial Positive Definite Functions Generated by Euclid's Hat," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 88-119, April.
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    Cited by:

    1. Promit Ghosal & Bodhisattva Sen, 2017. "On Univariate Convex Regression," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 215-253, August.
    2. Balabdaoui, Fadoua & Durot, Cécile, 2015. "Marshall lemma in discrete convex estimation," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 143-148.

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