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Complexity penalized support estimation

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  • Klemelä, Jussi

Abstract

We consider the estimation of the support of a probability density function with iid observations. The estimator to be considered is a minimizer of a complexity penalized excess mass criterion. We present a fast algorithm for the construction of the estimator. The estimator is able to estimate supports which consists of disconnected regions. We will prove that the estimator achieves minimax rates of convergence up to a logarithmic factor simultaneously over a scale of Hölder smoothness classes for the boundary of the support. The proof assumes a sharp boundary for the support.

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  • Klemelä, Jussi, 2004. "Complexity penalized support estimation," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 274-297, February.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:2:p:274-297
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    1. Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
    2. Hall, Peter & Nussbaum, Michael & Stern, Steven E., 1997. "On the Estimation of a Support Curve of Indeterminate Sharpness," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 204-232, August.
    3. Dominique Deprins & Léopold Simar & Henry Tulkens, 2006. "Measuring Labor-Efficiency in Post Offices," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 285-309, Springer.
    4. Korostelev, A. P. & Simar, L. & Tsybakov, A. B., 1995. "Estimation of monotone boundaries," LIDAM Reprints CORE 1178, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Hardle, W. & Park, B. U. & Tsybakov, A. B., 1995. "Estimation of Non-sharp Support Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 205-218, November.
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    Cited by:

    1. Biau, Gérard & Cadre, Benoît & Pelletier, Bruno, 2008. "Exact rates in density support estimation," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2185-2207, November.
    2. Baíllo, Amparo & Cuevas, Antonio, 2004. "Image estimators based on marked bins," DES - Working Papers. Statistics and Econometrics. WS ws045114, Universidad Carlos III de Madrid. Departamento de Estadística.

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