Robust Estimation of Regression Coefficients with Outliers

  • Pimpan Ampanthong Department of Mathematics, Faculty of Science and Technology, Rajamangala University of Technology Suvarnabhumi, Supan Buri Campus, 72130, Thailand.
  • Prachoom Suwattee School of Applied Statistics, National Institute of Development Administration, Bangkapi, Bangkok, 10240, Thailand.
Keywords: influence functions, M-estimates, multiple linear regression, outliers, robust regression, weighted least-squares

Abstract

This study concentrates on the construction of weights for the estimation of regression coefficients in multiple linear regression with outliers using a new proposed influence function. Set of weights, modified weights one (MW1) are obtained from newly modified influence function. The proposed estimates are applied in the M-estimator of the regression coefficients with outliers and compared to ordinary least-squares (OLS) and other M-estimates by simulation. Results of the estimates indicate that the new weights out perform the least squares estimates and the other M-estimates. As for X-outliers and XY-outliers, it is found that the proposed estimates using MW out perform the least squares estimates for all sample sizes. It also gives high values of R2 and low MSE at different percentages of outliers as well.
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