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Robust minimum information loss estimation

Author

Listed:
  • Lind, John C.
  • Wiens, Douglas P.
  • Yohai, Victor J.

Abstract

Two robust estimators of a matrix-valued location parameter are introduced and discussed. Each is the average of the members of a subsample–typically of covariance or cross-spectrum matrices–with the subsample chosen to minimize a function of its average. In one case this function is the Kullback–Leibler discrimination information loss incurred when the subsample is summarized by its average; in the other it is the determinant, subject to a certain side condition. For each, the authors give an efficient computing algorithm, and show that the estimator has, asymptotically, the maximum possible breakdown point. The main motivation is the need for efficient and robust estimation of cross-spectrum matrices, and they present a case study in which the data points originate as multichannel electroencephalogram recordings but are then summarized by the corresponding sample cross-spectrum matrices.

Suggested Citation

  • Lind, John C. & Wiens, Douglas P. & Yohai, Victor J., 2013. "Robust minimum information loss estimation," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 98-112.
    • Handle: RePEc:eee:csdana:v:65:y:2013:i:c:p:98-112
    DOI: 10.1016/j.csda.2012.06.011
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    References listed on IDEAS

    as
    1. Todorov, Valentin, 1992. "Computing the minimum covariance determinant estimator (MCD) by simulated annealing," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 515-525, November.
    2. Mitra, Amit & Kundu, Debasis & Agrawal, Gunjan, 2006. "Frequency estimation of undamped exponential signals using genetic algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1965-1985, December.
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