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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| Lenguaje: | Inglés |
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2007
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 08063caa a22007697a 4500 | ||
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| 001 | PAPER-6737 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518203627.0 | ||
| 008 | 190411s2007 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-33846669152 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 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 | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-33846669152&doi=10.1007%2fs10260-006-0029-1&partnerID=40&md5=c628df6cb19c860ed485c9a5281a57d9 |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10260-006-0029-1 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_16182510_v15_n3_p295_Boente |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16182510_v15_n3_p295_Boente |y Registro en la Biblioteca Digital |
| 961 | |a paper_16182510_v15_n3_p295_Boente |b paper |c PE | ||
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| 999 | |c 67690 | ||