Applying Bootstrap Robust Regression Method on Data with Outliers

  • Ahmed M. Mami Department of Statistics, Faculty of Science, University of Benghazi, Benghazi, +128, Libya
  • Abobaker M. Jaber Department of Statistics, Faculty of Science, University of Benghazi, Benghazi, +128, Libya
  • Osama S. Almabrouk Department of Statistics, Faculty of Science, University of Benghazi, Benghazi, +128, Libya
Keywords: regression analysis, outliers, robust regression, bootstrap


Identification and assessment of outliers have a key role in Ordinary Least Squares (OLS) regression analysis. This paper presents a robust two-stage procedure to identify outlying observations in regression analysis. The exploratory stage identifies leverage points and vertical outliers through a robust distance estimator based on Minimum Covariance Determinant (MCD). After deletion of these points, the confirmatory stage carries out an OLS analysis on the remaining subset of data and investigates the effect of adding back in the previously deleted observations. Cut-off points pertinent to different diagnostics are generated by bootstrapping and the cases are definitely labeled as good-leverage, bad leverage, vertical outliers and typical cases. This procedure is applied to four examples taken from the literature and it is effective in rightly pinpointing outlying observations, even in the presence of substantial masking. This procedure is able to identify and correctly classify vertical outliers, good and bad leverage points, through the use of jackknife-after-bootstrap robust cut-off points. Moreover its two stage structure makes it interactive and this enables the user to reach a deeper understanding of the dataset main features than resorting to an automatic procedure.


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