Abstract
An iterative algorithm for the robust M-estimation of the dispersion matrix of the form Γ + σ2 I p has been given. This algorithm converges after some steps and reduces the effect of outliers on the covariance matrix. The consistency and asymptotic normality of the estimator are established.
Similar content being viewed by others
References
Chen, H.-J., Gnanadesikan, R. and Kettenring, J. R. (1974). Statistical methods for grouping corporations, Sankhyā Ser. B, 36, 1–28.
Devlin, S. J., Gnanadesikan, R. and Kettenring, J. R. (1975). Robust estimation and outlier detection with correlation coefficients, Biometrika, 62, 531–545.
Gnanadesikan, R. and Kettenring, J. R. (1972). Robust estimates, residuals and outlier detection with multiresponse data, Biometrics, 28, 81–124.
Huber, P. J. (1967). The behavior of maximum likelihood estimates under non-standard conditions, Proc. Fifth Berkeley Symp. on Math. Statist. Prob., Vol. 1, 222–233, Univ. of California Press, Berkeley.
Huber, P. J. (1977a). Robust covariances, Statistical Decision Theory and Related Topics II (eds. Shanti S.Gupta and David S.Moore), 165–191, Academic Press, New York.
Huber, P. J. (1977b). Robust Statistical Procedures, Society for Industrial Applied Mathematics, Philadelphia.
Huber, P. J. (1981). Robust Statistics, Wiley, New York.
Jöreskog, K. G. (1967). Some contributions to maximum likelihood factor analysis, Psychometrika, 32, 444–482.
Kelker, D. (1970). Distribution theory of spherical distribution and a location scale parameter generalization, Sankhyā Ser. A, 44, 419–430.
Lawley, D. N. and Maxwell, A. E. (1963). Factor Analysis as a Statistical Method, Butterworths, London.
Marona, R. A. (1976). Robust M-estimators of multivariate location and scatter, Ann. Statist., 4, 51–67.
Mosteller, F. and Tukey, J. W. (1977). Data Analysis and Regression, Addison-Wesley, Reading, Massachusetts.
Rao, C. R. (1982). Matrix derivatives and its application to statisties, Encyclopedia of Statistical Science, Vol. 5 (eds. SamuelKotz and Norman L.Johnson), 320–325, Wiley, New York.
Rao, C. R. (1983). Linear Statistical Inference and Its Applications, Wiley, New York.
Von-Neumann, J. (1937). Some matrix inequalities and metrization of metric space, Tomsk Univ. Rev., 1, 286–300.
Wolfowitz, J. (1954). Generalization of the theorem of Glivenko-Cantelli, Ann. Math. Statist., 25, 131–138.
Zhao, L. C., Krishnaiah, P. R. and Bal, Z. D. (1986a). On detection of the number of signals in presence of white noise, J. Multivariate Anal., 20, 1–25.
Zhao, L. C., Krishnaiah, P. R. and Bai, Z. D. (1986b). On detection of the number of signals when the noise covariance matrix is arbitrary, J. Multivariate Anal., 20, 26–49.
Author information
Authors and Affiliations
About this article
Cite this article
Bhandapy, M. Robust M-estimation of a dispersion matrix with a structure. Ann Inst Stat Math 43, 689–705 (1991). https://doi.org/10.1007/BF00121648
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00121648