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Image estimators based on marked bins

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  • Baíllo, Amparo
  • Cuevas, Antonio

Abstract

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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  • 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.
  • Handle: RePEc:cte:wsrepe:ws045114
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    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/217/ws045114.pdf?sequence=1
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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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