Influence functions of two families of robust estimators under proportional scatter matrices

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-...

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Autor principal: Boente, G.
Otros Autores: Critchley, F., Orellana, L.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2007
Acceso en línea:Registro en Scopus
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100 1 |a Boente, G. 
245 1 0 |a Influence functions of two families of robust estimators under proportional scatter matrices 
260 |c 2007 
270 1 0 |m Boente, G.; Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Buenos Aires, C1428EHA, Argentina; email: gboente@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Boente, G., Orellana, L., A robust approach to common principal components (2001) Statistics in genetics and in the environmental sciences, pp. 117-145. , Fernholz LT, Morgenthaler S, Stahel W eds, Birkhäuser Verlag AG, Basel, pp 
504 |a Boente, G., Orellana, L., Robust plug-in estimators in proportional scatter models (2004) J Stat Plann Inference, 122, pp. 95-110 
504 |a Boente, G., Pires, A., Rodrigues, I., Influence functions and outlier detection under the common principal components model (2002) Biometrika, 89, pp. 861-875 
504 |a Boente, G., Critchley, F., Orellana, L., (2004) Influence functions for robust estimators, , http://www.ic.fcen.uba.ar/ preprints/boecriore.pdf, under proportional scatter matrices 
504 |a Boente, G., Pires, A., Rodrigues, I., General projection-pursuit estimators for the common principal components model: Influence functions and Monte Carlo study (2006) J Multivariate Anal, 97, pp. 124-147 
504 |a Croux, C., Haesbroeck, G., Principal component analysis based on robust estimators of the covariance or correlation matrix: Influence functions and efficiencies (2000) Biometrika, 87, pp. 603-618 
504 |a Croux, C., Ruiz-Gazen, A., A fast algorithm for robust principal components based on projection pursuit (1996) Compstat: Proceedings in computational statistics, pp. 211-217. , Prat A ed, Physica-Verlag, Heidelberg, pp 
504 |a Croux, C., Ruiz-Gazen, A., High breakdown estimators for principal components: The projection-pursuit approach revisited (2005) J multivariate Anal, 95, pp. 206-226. , pdf 
504 |a Donoho, D.L., (1982) Breakdown properties of multivariate location estimators. PhD qualifying paper, , Harvard University 
504 |a Eriksen, P.S., Proportionality of covariance matrices (1987) Ann Statist, 15, pp. 732-748 
504 |a Flury, B., Common principal components in groups (1984) J Am Stat Assoc, 79, pp. 892-898 
504 |a Flury, B., Proportionality of k covariance matrices (1986) Stat Probab Lett, 4, pp. 29-33 
504 |a Flury, B., (1988) Common principal components and related multivariate models, , Wiley, New York 
504 |a Flury, B., Schmid, M., Quadratic discriminant functions with constraints on the covariance matrices: Some asymptotic results (1992) J Multivariate Anal, 40, pp. 244-261 
504 |a Flury, B., Schmid, M., Narayanan, A., Error rates in quadratic discrimination with constraints on the covariance matrices (1994) J Classification, 11, pp. 101-120 
504 |a Guttman, I., Kim, D.Y., Olkin, I., Statistical inference for constants of proportionality (1985) Multivariate analysis-VI, pp. 257-280. , Krishnaiah PR ed, North-Holland, New York, pp 
504 |a Khatri, C.G., Some distribution problems connected with the characteristic roots of S1S2 -1 (1967) Ann Math Stat, 38, pp. 944-948 
504 |a Kim, D.Y., Statistical inference for constants of proportionality between covariance matrices (1971), Technical Report 59, Standford University, Department of Statistics, Stanford; Manly, B.F., Rayner, J.C.W., The comparison of sample covariance matrices using likelihood ratio tests (1987) Biometrika, 74, pp. 841-847 
504 |a Maronna, R.A., Robust M-estimators of multivariate location and scatter (1976) Ann Stat, 4, pp. 51-67 
504 |a Novi Inverardi, P.L., Flury, B., Robust estimation of common principal components (1992) Quaderni di Statistica e Matematica Applicata alle Scienze Economico-Social, 14, pp. 49-79 
504 |a Owen, A., A neighborhood-based classifier for landsat data (1984) Canad J of Statist, 12, pp. 191-200 
504 |a Pillai, K.C.S., Al-Ani, S., Jouris, G.M., On the distribution of the ratios of the roots of a covariance matrix and Wilks' criterion for tests of three hypotheses (1969) Ann Math Stat, 40, pp. 2033-2040 
504 |a Pires, A.M., Branco, J., Partial influence functions (2002) J Multivariate Anal, 83, pp. 451-468 
504 |a Rao, C.R., Likelihood tests for relationships between covariance matrices (1983) Studies in econometrics, time series and multivariate statistics, pp. 529-543. , Karlim S, Ameniya T, Goodman LA eds, Academic, New York, pp 
504 |a Stahel, W., (1981) Robust estimation: Infinitesimal optimality and covariance matrix estimation, , in German Thesis, ETH, Zurich 
520 3 |a 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. © 2006 Springer-Verlag.  |l eng 
536 |a Detalles de la financiación: Universidad de Buenos Aires, PID 5505 
536 |a Detalles de la financiación: Fundación Antorchas, X094 
536 |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica 
536 |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, PAV 120, PICT 21407 
536 |a Detalles de la financiación: Acknowledgment The authors would like to thank David Tyler for stimulating discussions during the preparation of this paper. They also would like to thank the Referees for their valuable comments and suggestions that lead to improve the presentation of the paper. This research was partially supported by Grants 13900-6 from the Fundación Antorchas, X094 from University of Buenos Aires, PID 5505 from CONICET and PAV 120 and PICT 21407 from ANPCYT, Argentina. 
593 |a Universidad de Buenos Aires, CONICET, Buenos Aires, Argentina 
593 |a Open University, Milton Keynes, United Kingdom 
593 |a Universidad de Buenos Aires, Buenos Aires, Argentina 
593 |a Harvard School of Public Health, Harvard University, Boston, MA, United States 
593 |a Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Buenos Aires, C1428EHA, Argentina 
690 1 0 |a PARTIAL INFLUENCE CURVES 
690 1 0 |a PROJECTION-PURSUIT 
690 1 0 |a PROPORTIONAL SCATTER MODELS 
690 1 0 |a ROBUST ESTIMATION 
690 1 0 |a ROBUST SCATTER MATRICES 
700 1 |a Critchley, F. 
700 1 |a Orellana, L. 
773 0 |d 2007  |g v. 15  |h pp. 295-327  |k n. 3  |p Stat. Methods and Appl.  |x 16182510  |t Statistical Methods and Applications 
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856 4 0 |u https://hdl.handle.net/20.500.12110/paper_16182510_v15_n3_p295_Boente  |y Handle 
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