Robust minimum information loss estimation

• Published in: Computational statistics & data analysis Vol. 65; pp. 98 - 112
• Main Authors: Lind, John C., Wiens, Douglas P., Yohai, Victor J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2013
• Subjects: Algorithms; Breakdown; case studies; Covariance; Cross-spectrum matrix; Electroencephalogram recording; electroencephalography; Genetic algorithm; Minimum covariance determinant; Minimum information loss determinant estimate; motivation; Spectrum; Trimmed minimum information loss estimate; Minimum covariance determinant; Covariance; Genetic algorithm; Cross-spectrum matrix; Minimum information loss determinant estimate; Breakdown; Electroencephalogram recording; Trimmed minimum information loss estimate; Spectrum
• ISSN: 0167-9473; 1872-7352; 1872-7352
• DOI: 10.1016/j.csda.2012.06.011

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.