Construction of composite indices in presence of outliers

Mishra, SK (2008): Construction of composite indices in presence of outliers.

Abstract

Effects of outliers on mean, standard deviation and Pearson’s correlation coefficient are well known. The Principal Components analysis uses Pearson’s product moment correlation coefficients to construct composite indices from indicator variables and hence may be very sensitive to effects of outliers in data. Median, mean deviation and Bradley’s coefficient of absolute correlation are less susceptible to effects of outliers. This paper proposes a method to obtain composite indices by maximization of the sum of absolute Bradley’s correlation coefficients between the indicator variable and the derived composite index.

• Item Type: MPRA Paper
• Language: English
• Keywords: Composite index; Principal Components analysis; absolute; Bradley’s correlation coefficient; outliers; median; mean deviation; Differential Evolution; global optimization
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

References

• Bradley, C. (1985) “The Absolute Correlation”, The Mathematical Gazette, 69(447), pp. 12-17. • Hampel, F. (2001) “Robust Statistics: a Brief Introduction and Overview”, ftp://ftp.stat.math.ethz.ch/Research-Reports/94.pdf • Mishra, S.K. (2007a): “Performance of Differential Evolution Method in Least Squares Fitting of Some Typical Nonlinear Curves” Journal of Quantitative Economics, 5(1), pp. 140-177. • Mishra, S.K. (2007b): “Least Squares Estimation of Joint Production Functions by the Differential Evolution method of Global Optimization.” Economics Bulletin, 3(51), pp. 1-13. • Mishra, S.K. (2007c) "Construction of an Index by Maximization of the Sum of its Absolute Correlation Coefficients with the Constituent Variables" SSRN: http://ssrn.com/abstract=989088 • Shevlyakov, G.L. (1997) “On Robust Estimation of a Correlation Coefficient”, Journal of Mathematical Sciences, 83(3), pp. 434-438.