A robust regression methodology via M-estimation |
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Authors: | Tao Yang Colin M Gallagher |
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Institution: | Department of Mathematical Sciences, Clemson University, Clemson, SC, USA |
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Abstract: | A robust regression methodology is proposed via M-estimation. The approach adapts to the tail behavior and skewness of the distribution of the random error terms, providing for a reliable analysis under a broad class of distributions. This is accomplished by allowing the objective function, used to determine the regression parameter estimates, to be selected in a data driven manner. The asymptotic properties of the proposed estimator are established and a numerical algorithm is provided to implement the methodology. The finite sample performance of the proposed approach is exhibited through simulation and the approach was used to analyze two motivating datasets. |
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Keywords: | Asymmetric exponential power distribution Linear regression M-estimation Quantile regression Robust regression |
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