Abstract
Robust estimation of the correlation coefficient of a bivariate normal distribution is considered in the case of a contamination scheme. A number of conventional robust estimates are studied, and some new estimates are proposed. Their properties are examined on finite samples and in asymptotics with the use of Monte-Carlo and the influence functions techniques correspondingly. It is shown that one of the proposed estimates called a median correlation coefficient has high robustness properties.
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References
N. Blomqvist, “On a measure of dependance between two random variables,”Ann. Math. Statist.,21, No. 4, 593–600 (1950).
S. J. Devlin, R. Gnanadesikan, and J. R. Kettenring, “Robust estimation and outlier detection with correlation coefficient,”Biometrika,62, No. 3, 531–545 (1975).
R. Gnanadesikan and J. R. Kettenring, “Robust estimates, residuals and outlier detection with multiresponce data,”Biometrics,28, No. 1, 81–124 (1972).
F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel,Robust Statistics. The Approach Based on Influence Functions, Wiley, New York (1986).
P. J. Huber, “Robust estimation of a location parameter,”Ann. Math. Statist.,36, No. 1, 1–72 (1964).
P. J. Huber,Bobust Statistics, Wiley, New York (1981).
C. Spearman, “The proof and measurement of association between two things,”Am. J. Psychol.,15, 88–93 (1904).
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Proceedings of the XVII Seminar on Stability Problems for Stochastic Models. Kazan, Russian, 1995, Part II.
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Shevlyakov, G.L. On Robust estimation of a correlation coefficient. J Math Sci 83, 434–438 (1997). https://doi.org/10.1007/BF02400929
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DOI: https://doi.org/10.1007/BF02400929