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A set-indexed process in a two-region image

Author

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  • Müller, Hans-Georg
  • Song, Kai-Sheng

Abstract

We investigate the problem of edge estimation in a two-region image in the setting of a fixed design regression model. The edge estimation problem is equivalent to estimating one of the plateau sets where the regression function is constant, and we define a global set-valued estimator by finding the partition which maximizes a weighted distance measure. An investigation of the weak convergence of the random sets generated by this estimator shows that a properly scaled stochastic process in symmetric differences between estimated and true partitions converges in the limit to a set-indexed Brownian motion with drift in d.

Suggested Citation

  • Müller, Hans-Georg & Song, Kai-Sheng, 1996. "A set-indexed process in a two-region image," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 87-101, March.
    • Handle: RePEc:eee:spapps:v:62:y:1996:i:1:p:87-101
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    Cited by:

    1. Estate Khmaladze & Wolfgang Weil, 2018. "Fold-up derivatives of set-valued functions and the change-set problem: A Survey," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 1-38, February.
    2. V. Yu. Bogdanskii & O. I. Klesov & I. Molchanov, 2021. "Uniform Strong Law of Large Numbers," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 461-470, June.

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