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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood.

Howard D Bondell1, Leonard A Stefanski

  • 1Department of Statistics, North Carolina State University, Box 8203, Raleigh, NC 27695, U.S.A.

Journal of the American Statistical Association
|August 27, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a novel robust regression estimator balancing efficiency and outlier resistance. Simulations show it performs well in small samples and handles outliers effectively, outperforming existing methods.

Keywords:
Asymptotic efficiencyBreakdown pointConstrained optimizationEfficient estimationEmpirical likelihoodExponential tiltingLeast trimmed squaresRobust regressionWeighted least squares

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Area of Science:

  • Statistics
  • Econometrics
  • Data Science

Background:

  • Robust statistics aims for efficiency and outlier resistance, which are often conflicting goals.
  • Existing robust regression estimators face challenges in simultaneously achieving high efficiency and strong outlier resistance.

Purpose of the Study:

  • To develop and analyze a new linear regression estimator that closely achieves both large- and finite-sample efficiency and outlier resistance.
  • To evaluate the performance of the proposed estimator against existing robust regression techniques.

Main Methods:

  • The proposed estimator is linked to generalized empirical likelihood.
  • Robustness is achieved by constraining the sum of weighted squared residuals.
  • Theoretical properties include maximum finite-sample replacement breakdown point and full asymptotic efficiency for normal errors.

Main Results:

  • The new estimator demonstrates high efficiency for small sample sizes.
  • It exhibits comparable resistance to outliers relative to existing robust regression estimators.
  • Empirical application on a real dataset with outliers validates its performance.

Conclusions:

  • The developed robust regression estimator offers a favorable balance between efficiency and outlier resistance.
  • It presents a promising alternative for regression analysis in the presence of outliers, especially in small samples.