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Estimation of a "k"-monotone density: characterizations, consistency and minimax lower bounds


  • Fadoua Balabdaoui
  • Jon A. Wellner


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  • Fadoua Balabdaoui & Jon A. Wellner, 2010. "Estimation of a "k"-monotone density: characterizations, consistency and minimax lower bounds," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 45-70.
  • Handle: RePEc:bla:stanee:v:64:y:2010:i:1:p:45-70

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    References listed on IDEAS

    1. Dragi Anevski, 2003. "Estimating the Derivative of a Convex Density," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(2), pages 245-257.
    2. Piet Groeneboom & Geurt Jongbloed & Jon A. Wellner, 2008. "The Support Reduction Algorithm for Computing Non-Parametric Function Estimates in Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 385-399.
    3. Jongbloed, Geurt, 2000. "Minimax lower bounds and moduli of continuity," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 279-284, November.
    4. 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. Chee, Chew-Seng & Wang, Yong, 2016. "Nonparametric estimation of species richness using discrete k-monotone distributions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 107-118.
    2. Chew-Seng Chee, 2016. "Modelling of count data using nonparametric mixtures," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 239-257, July.
    3. Chee, Chew-Seng & Wang, Yong, 2014. "Least squares estimation of a k-monotone density function," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 209-216.
    4. Chee, Chew-Seng & Wang, Yong, 2013. "Minimum quadratic distance density estimation using nonparametric mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 1-16.

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