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This paper proposes an adaptive penalized weighted mean regression foroutlier detection of high-dimensional data. In comparison to existingapproaches based on the mean shift model, the proposed estimators demonstraterobustness against outliers present in both response variables and/orcovariates. By utilizing the adaptive Huber loss function, the proposed methodis effective in high-dimensional linear models characterized by heavy-tailedand heteroscedastic error distributions. The proposed framework enablessimultaneous and collaborative estimation of regression parameters and outlierdetection. Under regularity conditions, outlier detection consistency andoracle inequalities of robust estimates in high-dimensional settings areestablished. Additionally, theoretical robustness properties, such as thebreakdown point and a smoothed limiting influence function, are ascertained.Extensive simulation studies and a breast cancer survival data are used toevaluate the numerical performance of the proposed method, demonstratingcomparable or superior variable selection and outlier detection capabilities.

High-dimensional outlier detection and variable selection via adaptive weighted mean regression