Influence functions of two families of robust estimators under proportional scatter matrices |
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| Authors: | Graciela Boente Frank Critchley Liliana Orellana |
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| Institution: | (1) Universidad de Buenos Aires and CONICET, Buenos Aires, Argentina;(2) The Open University, Milton Keynes, UK;(3) Universidad de Buenos Aires, Buenos Aires, Argentina and Harvard School of Public Health, Harvard University, Boston, MA, USA;(4) Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón 2, Buenos Aires, C1428EHA, Argentina |
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| Abstract: | In this paper, under a proportional model, two families of robust estimates for the proportionality constants, the common
principal axes and their size are discussed. The first approach is obtained by plugging robust scatter matrices on the maximum
likelihood equations for normal data. A projection- pursuit and a modified projection-pursuit approach, adapted to the proportional
setting, are also considered. For all families of estimates, partial influence functions are obtained and asymptotic variances
are derived from them. The performance of the estimates is compared through a Monte Carlo study. |
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| Keywords: | Robust estimation Robust scatter matrices Projection-pursuit Proportional scatter models Partial influence curves |
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