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Support vector regression (SVR) is now a well-established method for estimating real-valued functions. However, the standard SVR is not effective to deal with severe outlier contamination of both response and predictor variables commonly encountered in numerous real applications. In this paper, we present a bounded influence SVR, which downweights the influence of outliers in all the regression variables. The proposed approach adopts an adaptive weighting strategy, which is based on both a robust adaptive scale estimator for large regression residuals and the statistic of a ldquokernelizedrdquo hat matrix for leverage point removal. Thus, our algorithm has the ability to accurately extract the dominant subset in corrupted data sets. Simulated linear and nonlinear data sets show the robustness of our algorithm against outliers. Last, chemical and astronomical data sets that exhibit severe outlier contamination are used to demonstrate the performance of the proposed approach in real situations.