Malaysian Journal of Mathematical Sciences, September 2016, Vol. 10, No. 3
Detection of High Leverage Points Using a Nonparametric Cut-off Point for the Robust Mahalanobis Distance
A. H. M. Rahmatullah Imon and M. Rasheduzzaman Apu
Corresponding Email: imon_ru@yahoo.com
Received date: -
Accepted date: -
Abstract:
Mahalanobis distance (MD) is a widely used multivariate technique for measuring dispersion. Rousseuw and Leroy (1987) advocated using MD as a measure of high leverage points in linear regression. Since MD's are non-robust in the presence of high leverage points they suggested using robust version of Mahalanobis distance. They also proposed a cut-off point for MD's which follows a square root of Chi-square distribution with the degrees of freedom equals to the dimension of the explanatory variables. But we see a major problem in it. In regression we do not assume normality assumption for the explanatory variables, sometimes the explanatory variables may be indicator or categorical variables. Moreover, the explanatory variables are treated as fixed variables hence a chi-square cut-off point is not appropriate. In this paper we propose a nonparametric cut-off point for the robust Mahalanobis distance. This cut-off point does not require any distributional assumption of the explanatory variables. We employ this method to several well-known data sets and observed that the proposed method performs much better than the existing methods.
Keywords: Leverage, Mahalanobis distance, MVE, Swamping
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