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Robust M ‐estimators of multivariate location and scatter in the presence of asymmetry
Author(s) -
Wiens D. P.,
Zheng Z.
Publication year - 1986
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314661
Subject(s) - estimator , minimax , mathematics , asymmetry , location parameter , distribution (mathematics) , statistics , mathematical optimization , mathematical analysis , physics , quantum mechanics
Robust estimation of location vectors and scatter matrices is studied under the assumption that the unknown error distribution is spherically symmetric in a central region and completely unknown in the tail region. A precise formulation of the model is given, an analysis of the identifiable parameters in the model is presented, and consistent initial estimators of the identifiable parameters are constructed. Consistent and asymptotically normal M ‐estimators are constructed (solved iteratively beginning with the initial estimates) based on “influence functions” which vanish outside specified compact sets. Finally M ‐estimators which are asymptotically minimax (in the sense of Huber) are derived.