Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Weighted Least Absolute Error Estimation of Regression Parameters

  • Song, Moon-Sup (Department of Computer Science and Statistics, Seoul National University)
  • Published : 1979.06.01
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Abstract

In the multiple linear regression model a class of weighted least absolute error estimaters, which minimize the sum of weighted absolute residuals, is proposed. It is shown that the weighted least absolute error estimators with Wilcoxon scores are equivalent to the Koul's Wilcoxon type estimator. Therefore, the asymptotic efficiency of the proposed estimator with Wilcoxon scores relative to the least squares estimator is the same as the Pitman efficiency of the Wilcoxon test relative to the Student's t-test. To find the estimates the iterative weighted least squares method suggested by Schlossmacher is applicable.

Keywords

References

  1. The Annals of Mathematical Statistics v.38 Estimates of regression parameters based on rank tests Adichie,J.N.
  2. Journal of the American Statistical Association v.73 Asymptotic theory of least absolute error regression Basset,G.Jr.;Koenker,R.
  3. The Annals of Statistics v.1 On some analogues to linear combinations of order statistics and linear model Bickel,P.J.
  4. The Annals of Mathematical Statistics v.34 Estimates of location based on rank tests Hodges,J.L.;Lehmann,E.L.
  5. The Annals of Mathematical Statistics v.35 Robust estimation of a location parameter Huber,P.J.
  6. The Annals of Statistics v.1 Robust regression: Asymptotics, conjectures and Monte Carlo Huber,P.J.
  7. The Annals of Mathematical Statistics v.43 Estimating regression coefficients by minimizing the dispersion of the residuals Jaeckel,L.A.
  8. The Annals of Mathematical Statistics v.42 Nonparametric estimate of the regression coefficients Jureckove,J.
  9. The Annals of Mathematical Statistics v.40 Asymptotic behavior of Wilcoxon type confidence regions in multiple linear rgression Koul,H.L.
  10. Journal of the American Statistical Association v.68 An iterative technique for absolute deviations curve fitting Schlossmacher,E.J.
  11. The Annals of Statistics v.6 Weighted median regression estimates Scholz,F.W.
  12. Journal of the American Statistical Association v.63 Estimates of the regression coefficients based on Kendall's tau Sen,P.K.
  13. Journal of the American Statisttical Association v.73 Weighted rank statistics for simple linear regression Sievers,G.L.