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On minimax rates of convergence in image models under sequential design

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  • Korostelev, Alexander

Abstract

A binary image model is studied with a Lipschitz edge function. The indicator function of the image is observed in random noise at n design points that can be chosen sequentially. The asymptotically minimax rate as n-->[infinity] is found in estimating the edge function, and an asymptotically optimal algorithm is described.

Suggested Citation

  • Korostelev, Alexander, 1999. "On minimax rates of convergence in image models under sequential design," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 369-375, July.
  • Handle: RePEc:eee:stapro:v:43:y:1999:i:4:p:369-375
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    References listed on IDEAS

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    1. Nolan, D., 1992. "Asymptotics for multivariate trimming," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 157-169, August.
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    5. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    6. Rousseeuw, Peter J., 1993. "A resampling design for computing high-breakdown regression," Statistics & Probability Letters, Elsevier, vol. 18(2), pages 125-128, September.
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    Cited by:

    1. Kim, Jae-Chun & Korostelev, Alexander, 2000. "Rates of convergence for the sup-norm risk in image models under sequential designs," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 391-399, February.

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