Robust minimum information loss estimation

JOHN C. LIND; DOUGLAS P. WIENS; VICTOR J. YOHAI

COMPUTATIONAL STATISTICS AND DATA ANALYSIS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2013 vol. 65 p. 98 - 112

0167-9473

Many existing methods for functional regression are based on the minimization of an L2 norm of the residuals and are therefore sensitive to atypical observations, which may affect the predictive power and/or the smoothness of the resulting estimate. A robust version of a spline-based estimate is presented, which has the form of an MM estimate, where the L2 loss is replaced by a bounded loss function. The estimate can be computed by a fast iterative algorithm. The proposed approach is compared, with favorable results, to the one based on L2 and to both classical and robust Partial Least Squares through an example with high-dimensional real data and a simulation study 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 crossspectrum 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.