Keywords: multicollinearity, outliers, Surrogate Ridge estimator, M-estimator, MM- estimator, Big Data.
One of important issues in the big data is the analytic approach to learn from data for optimal decision, The most frequently used analytic approach is regression analysis . The classical Least Squares estimators have optimal properties if the Gauss-Markov assumptions were satisfied. Multicollinearity and outliers are commonly occurring problems. The problem is further complicated when both outliers and multicollinearity are presented in the data simultaneously. Several techniques are available in the literature which deals with the problem of multicollinearity and outliers in the data independently. However, very few techniques were presented for the problem of multicollinearity and outliers simultaneously. Silvapulle (1991) proposed a ridge M-estimator (RME) as a robust estimator by shrinking the M- estimator (ME) and robustify the biasing parameter (k) of Hoerl and Kennard (1970a,b). Arslan and Billor (2000) proposed a Liu M-estimator (LME) as a robust estimator by shrinking the M- estimator (ME) and robustify the biasing parameter (d) of Liu (1993. Habshah and Lau (2009) proposed a method called Latent Root – M based Regression (LRMB) because they employed the weight of the M-estimator in the weighted correlation matrix. Jadhav and Kashid (2016) proposed a linearized ridge M-estimator (LRME) as a robust estimator by shrinking the M- estimator (ME) and robustify the biasing parameter (D) of Gao and Liu (2011). In this study, we present two new estimators one called Surrogate Ridge M-estimator (SRME) as a robust estimator which combats the problem of simultaneous occurrence of multicollinearity and outliers in y-direction, and other called Surrogate Ridge MM-estimator (SRMME) as a robust estimator which combats the problem of simultaneous occurrence of multicollinearity and outliers in Y and X directions. A real data examples and a simulation study is presented to illustrate the performance of the newly proposed estimators. Results of