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Simple consistent cluster methods based on redescending M-estimators with an application to edge identification in images

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  • Müller, Christine H.
  • Garlipp, Tim

Abstract

We use the local maxima of a redescending M-estimator to identify cluster, a method proposed already by Morgenthaler (in: H.D. Lawrence, S. Arthur (Eds.), Robust Regression, Dekker, New York, 1990, pp. 105-128) for finding regression clusters. We work out the method not only for classical regression but also for orthogonal regression and multivariate location and show that all three approaches are special cases of a general approach which includes also other cluster problems. For the general case we show consistency for an asymptotic objective function which generalizes the density in the multivariate case. The approach of orthogonal regression is applied to the identification of edges in noisy images.

Suggested Citation

  • Müller, Christine H. & Garlipp, Tim, 2005. "Simple consistent cluster methods based on redescending M-estimators with an application to edge identification in images," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 359-385, February.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:2:p:359-385
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    References listed on IDEAS

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    1. Hennig, Christian, 2003. "Clusters, outliers, and regression: fixed point clusters," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 183-212, July.
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    Cited by:

    1. Garlipp, T. & Muller, C.H., 2006. "Detection of linear and circular shapes in image analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1479-1490, December.
    2. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.
    3. Bai, Xiuqin & Yao, Weixin & Boyer, John E., 2012. "Robust fitting of mixture regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2347-2359.
    4. Christoph Gollob & Tim Ritter & Arne Nothdurft, 2020. "Comparison of 3D Point Clouds Obtained by Terrestrial Laser Scanning and Personal Laser Scanning on Forest Inventory Sample Plots," Data, MDPI, vol. 5(4), pages 1-13, October.
    5. Li, Ting & Song, Xinyuan & Zhang, Yingying & Zhu, Hongtu & Zhu, Zhongyi, 2021. "Clusterwise functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).

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