The main purpose of this paper is to formulate a robust correlation coefficient for high dimensional data in the presence of multivariate outliers. The proposed method is compared with the existing robust bivariate correlation based on Adjusted Winsorization data and the well-known Pearson's correlation coefficient. The performance of our proposed method is investigated using artificial data and simulation study. An important implication of these findings is that the robust correlation based on RFCH estimator is more reliable and more efficient than the existing methods in all type of contamination scenarios.

The desirability function approach is commonly used in industry to tackle multiple response optimization problems. The shortcoming of this approach is that the variability in each predicted response is ignored. It is now evident that the actual response may fall outside the acceptable region even though the predicted response at the optimal solution has a high overall desirability score. An augmented approach to the desirability function (AADF) is put forward to rectify this problem. Nevertheless the AADF is easily affected by outliers since the AADF is constructed based on the Ordinary Least Squares (OLS) estimate which is not resistant to outliers. As an alternative, we propose a robust MM-estimator to estimate the parameters of the Response Surface Model (RSM) and incorporated the estimated parameters in the augmented approach framework. A numerical example is presented to assess the performance of the AADF -MM based method. The numerical results signify that the AADF-MM based is more efficient than the AADF-OLS based method.

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