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A Robust Regression Methodology via M-estimation.

Tao Yang1, Colin M Gallagher1, Christopher S McMahan1

  • 1Department of Mathematical Sciences, Clemson University.

Communications in Statistics: Theory and Methods
|February 26, 2021
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Summary
This summary is machine-generated.

This study introduces a robust regression method using M-estimation, offering reliable analysis for various data distributions by adapting to skewness and tail behavior. The approach ensures accurate regression parameter estimates through data-driven objective functions.

Keywords:
Asymmetric exponential power distributionLinear regressionM-estimationQuantile regressionRobust regression

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Area of Science:

  • Statistics
  • Econometrics

Background:

  • Traditional regression methods are sensitive to outliers and non-normal error distributions.
  • Robust statistical methods are needed for reliable data analysis in the presence of distributional deviations.

Purpose of the Study:

  • To propose a novel robust regression methodology using M-estimation.
  • To develop an approach that adapts to the tail behavior and skewness of error distributions.
  • To provide a reliable regression analysis applicable to a broad class of distributions.

Main Methods:

  • Utilizing M-estimation for robust regression parameter estimation.
  • Employing a data-driven approach to select the objective function for estimation.
  • Establishing asymptotic properties of the proposed M-estimator.
  • Developing a numerical algorithm for practical implementation.

Main Results:

  • The proposed M-estimation method demonstrates robustness to deviations from normality in error terms.
  • The data-driven selection of the objective function enhances adaptability to different error distributions.
  • Asymptotic properties of the estimator are theoretically established.
  • Simulations confirm the good finite sample performance of the robust regression approach.

Conclusions:

  • The proposed M-estimation methodology provides a reliable and adaptable tool for robust regression analysis.
  • This approach is effective for datasets with non-standard error distributions, including skewed or heavy-tailed data.
  • The method offers a valuable alternative to traditional regression techniques when distributional assumptions are violated.