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Image Estimators Based On Marked Bins

  • Amparo Baíllo

    ()

  • Antonio Cuevas

    ()

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    The problem of approximating an “image” S in R^d from a random sample of points is considered. If S is included in a grid of square bins, a plausible estimator of S is defined as the union of the “marked” bins (those containing a sample point). We obtain convergence rates for this estimator and study its performance in the approximation of the border of S. The estimation of “digitalized” images is also addressed by using a Vapnik-Chervonenkis approach. The practical aspects of implementation are discussed in some detail, including some technical improvements on the estimator, whose performance is checked through simulated as well as real data examples.

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    File URL: http://docubib.uc3m.es/WORKINGPAPERS/WS/ws045114.pdf
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    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws045114.

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    Date of creation: Nov 2004
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    Handle: RePEc:cte:wsrepe:ws045114
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    1. Klemelä, Jussi, 2004. "Complexity penalized support estimation," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 274-297, February.
    2. Cuevas, Antonio & Fraiman, Ricardo, 1998. "On visual distances in density estimation: the Hausdorff choice," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 333-341, November.
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