Simultaneous robust estimation of multi-response surfaces in the presence of outliers

A robust approach should be considered when estimating regression coefficients in multi-response problems. Many models are derived from the least squares method. Because the presence of outlier data is unavoidable in most real cases and because the least squares method is sensitive to these types of points, robust regression approaches appear to be a more reliable and suitable method for addressing this problem. Additionally, in many problems, more than one response must be analyzed; thus, multi-response problems have more applications. The robust regression approach used in this paper is based on M-estimator methods. One of the most widely used weighting functions used in regression estimation is Huber's function. In multi-response surfaces, an individual estimation of each response can cause a problem in future deductions because of separate outlier detection schemes. To address this obstacle, a simultaneous independent multi-response iterative reweighting (SIMIR) approach is suggested. By presenting a coincident outlier index (COI) criterion while considering a realistic number of outliers in a multi-response problem, the performance of the proposed method is illustrated. Two well-known cases are presented as numerical examples from the literature. The results show that the proposed approach performs better than the classic estimation, and the proposed index shows efficiency of the proposed approach.