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Estimating the Derivative of a Convex Density

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  • Dragi Anevski

Abstract

We obtain a relation between the time between two bird‐catchings and the total resting period of a bird, leading to the problem of estimating the derivative of a convex density. We state a fundamental result on the nonparametric maximum likelihood estimator of a convex density. Further, we derive the optimal rate in the minimax risk sense for estimating the derivative of a convex density.

Suggested Citation

  • 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, May.
    • Handle: RePEc:bla:stanee:v:57:y:2003:i:2:p:245-257
    DOI: 10.1111/1467-9574.00229
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    Cited by:

    1. Pavlides, Marios G. & Wellner, Jon A., 2012. "Nonparametric estimation of multivariate scale mixtures of uniform densities," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 71-89.
    2. Fils-Villetard, A. & Guillou, A. & Segers, J., 2005. "Projection Estimates of Constrained Functional Parameters," Discussion Paper 2005-111, Tilburg University, Center for Economic Research.
    3. 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, February.
    4. Fils-Villetard, A. & Guillou, A. & Segers, J., 2005. "Projection Estimates of Constrained Functional Parameters," Other publications TiSEM fe25c070-c313-4369-a6a5-8, Tilburg University, School of Economics and Management.

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