Robust Estimators for the Correlation Measure to Resist Outliers in Data

Juthaphorn Sinsomboonthong

Abstract


The objective of this research was to propose a composite correlation coefficient to estimate the rank correlation coefficient of two variables. A simulation study was conducted using 228 situations for a bivariate normal distribution to compare the robustness properties of the proposed rank correlation coefficient with three estimators, namely, Spearman’s rho, Kendall’s tau and Plantagenet’s correlation coefficients when the data were contaminated with outliers. In both cases of non-outliers and outliers in the data, it was found that the composite correlation coefficient seemed to be the most robust estimator for all sample sizes, whatever the level of the correlation coefficient. 


Keywords


correlation coefficient; rank correlation coefficient; outliers; robustness; estimator

Full Text:

(PDF)

References


Neter J., Kutner M.H., Nachtsheim C.J. & Wasserman W., Applied Linear Statistical Models, ed. 4, Irwin, 1996.

Maturi T.A. & Elsayigh A., A comparison of Correlation Coefficients via A Three-step Bootstrap Approach, Journal of Mathematics Research, 2(2), pp. 3-10, 2010.

Sinsomboonthong J., Bias Correction in Estimation of the Population Correlation Coefficient, Kasetsart Journal (Natural Science), 47(3), pp. 453-459, 2013.

Aggarwal, C.C., Outlier Analysis, Springer-Verlag New York, 2013.

Abdullah, M.B., On A Robust Correlation Coefficient, The Statistician, 39, pp. 455-460, 1990.

Gideon, R.A. & Hollister, R.A, A Rank Correlation Coefficient Resistant to Outliers, Journal of the American Statistical Association, 82(398), pp. 656-666, 1987.

Wilcox, R., Introduction to Robust Estimation and Hypothesis Testing, ed. 3, Academic Press, 2014.

Shevlyakov, G. & Smirnov, A., Robust Estimation of the Correlation Coefficient: An Attempt of Survey, Austrian Journal of Statistics, 40(1&2), pp. 147-156, 2011.

Gibbons, J.D. & Chakroborti, S., Nonparametric Statistical Inference, ed. 5, Chapman & Hall/CRC, 2010.

Hollander, M., Wolfe, D.A. & Chicken, E., Nonparametric Statistical Methods, ed. 3, John Wiley, 2013.

Siegel, S. & Castellan, N.J., Nonparametric Statistics for the Behavioral Sciences, ed. 2, McGraw-Hill, 1988.

Evandt, O., Coleman, S., Ramalhoto, M.F. & Lottum, C.V., A Little-known Robust Estimator of the Correlation Coefficient and Its Use in A Robust Graphical Test for Bivariate Normality with Applications in the Aluminium Industry, Quality and Reliability Engineering International, 20, pp. 433-456, 2004.

Genest, C. & Plante, J.F., On Blest’s Measure of Rank Correlation, The Canadian Journal of Statistics, 31(1), pp. 35-52, 2003.

Blest, D.C., Rank Correlation – An Alternative Measure, Australian and New Zealand Journal of Statistics, 42(1), pp. 101-111, 2000.

Quenouille, M.H., Notes on Bias in Estimation, Biometrika, 43, pp. 353-360, 1956.

Tukey, J.W., Bias and Confidence in Not Quite Large Samples, Annals of Mathematical Statistics, 29, pp. 614-623, 1958.

Balakrishnan, N. & Tony Ng, H.K., Improved Estimation of the Correlation Coefficient in A Bivariate Exponential Distribution, Journal of Statistical Computation and Simulation, 68(2), pp. 173-184, 2001.

Smith, C.D. & Pontius, J.S., Jackknife Estimator of Species Richness with S PLUS, Journal of Statistical Software, 15, pp. 1-12, 2006.

Sinsomboonthong, J., Estimation of the Correlation Coefficient for a Bivariate Normal Distribution with Missing Data, Kasetsart Journal (Natural Science), 45(4), pp. 736-742, 2011.

Scarsini, M., On Measures on Concordance, Stochastica, 8, pp. 201-218, 1984.

Mood, A.M., Graybill, F.A. & Boes, D.C., Introduction to the Theory of Statistics, ed. 3, McGraw-Hill, 1974.

Barnett, V. & Lewis, T., Outliers in Statistical Data, ed. 3, John Wiley, 1995.




DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2016.48.3.7

Refbacks

  • There are currently no refbacks.


View my Stats

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.