Robust Estimation of the Correlation Coefficient: An Attempt of Survey
DOI:
https://doi.org/10.17713/ajs.v40i1&2.206Abstract
Various groups of robust estimators of the correlation coefficient are introduced. The performance of most prospective estimators is examined at contaminated normal distributions both on small and large samples, and the best of the proposed robust estimators are revealed.References
Atkinson, A., and Riani, M. (2000). Robust Diagnostics Regression Aalysis. New York: Springer.
Blomqvist, N. (1950). On a measure of dependence between two random variables. The Annals of Mathematical Statistics, 21, 593-600.
Devlin, S. J., Gnanadesikan, R., and Kettenring, J. R. (1975). Robust estimation and outlier detection with correlation coefficient. Biometrika, 62, 531-545.
Falk, M. (1998). A note on the correlation median for elliptical distributions. Journal of Multivariate Analysis, 67, 306-317.
Gnanadesikan, R., and Kettenring, J. R. (1972). Robust estimates, residuals and outlier detection with multiresponse data. Biometrics, 28, 81-124.
Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. A. (1986). Robust Statistics. The Approach Based on Influence Functions. New York: John Wiley.
Hawkins, D. M. (1980). The Identification of Outliers. London: Chapman & Hall.
Huber, P. J. (1981). Robust Statistics. New York: John Wiley.
Kendall, M. G., and Stuart, A. (1963). The Advanced Theory of Statistics. Inference and Relationship. London: Griffin.
Maronna, R., and Yohai, D. M. V. (2006). Robust Statistics. Theory and Methods. New York: John Wiley & Sons.
Pasman, V. R., and Shevlyakov, G. L. (1987). Robust methods of estimation of a correlation coefficient. Automation and Remote Control, ??, 332-340.
Rousseeuw, P. J. (1984). Least median of squares regression. Journal of the American Statistical Association, 79, 871-880.
Rousseeuw, P. J., and Croux, C. (1993). Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88, 1273-1283.
Rousseeuw, P. J., and Leroy, A. M. (1987). Robust regression and outlier detection. New York: John Wiley & Sons.
Shevlyakov, G. L., and Vilchevsky, N. O. (2002). Minimax variance estimation of a correlation coefficient for epsilon-contaminated bivariate normal distributions. Statistics and Probability Letters, 57, 91-100.
Spearman, C. (1904). The proof and measurement of association between two things. American Journal of Psychology, 15, 88-93.
Tukey, J. W. (1960). A survey of sampling from contaminated distributions. In I. Olkin (Ed.), Contributions to Probability and Statistics (p. 448-485). Stanford: Stanford University Press.
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