Influence Functions of Iteratively Reweighted Least Squares Estimators

References

• Andrews , D. F. , Bickel , P. J. , Hampel , F. R. , Huber , P. J. , Rogers , W. H. and Tukey , J. W. 1972 . Robust Estimates of Location: Survey and Advances , Princeton University Press .
   Google Scholar
• Bartle , R. 1976 . The Elements of Real Analysis, , 2nd ed. , New York : John Wiley .
   Google Scholar
• Beaton , A. E. and Tukey , J. W. 1974 . The Fitting of Power Series, Meaning Polynomials, Illustrated on Band Spectroscopic Data . Technometrics , 16 : 147 – 185 .
   Web of Science ®Google Scholar
• Bickel , P. J. 1973 . On Some Analogues to Linear Combinations of Order Statistics in the Linear Model . The Annals of Statistics , 1 : 597 – 616 .
   Web of Science ®Google Scholar
• Bickel , P. J. 1975 . One-Step Huber Estimates in the Linear Model . Journal of the American Statistical Association , 70 : 428 – 434 .
   Web of Science ®Google Scholar
• Coleman , D. , Holland , P. , Kaden , N. , Klema , V. and Peters , S. C. 1980 . A System of Subroutines for Iteratively Reweighted Least Squares Computations . ACM Transactions on Mathematical Software , 6 : 327 – 336 .
   Web of Science ®Google Scholar
• Cook , R. D. and Weisberg , S. 1982 . Residuals and Influence in Regression , New York : Chapman & Hall .
   Google Scholar
• Fair , R. C. 1974 . On the Robust Estimation of Econometric Models . Annals of Economic Social Measurement , 3 : 667 – 678 .
   Google Scholar
• Hampel , F. R. , Ronchetti , E. M. , Rousseeuw , P. J. and Stahel , W. F. 1986 . Robust Statistics, the Approach Based on Influence Functions , New York : John Wiley .
   Google Scholar
• Hinkley , D. 1977 . Jackknifing in Unbalanced Situations . Technometrics , 19 : 285 – 292 .
   Web of Science ®Google Scholar
• Holland , P. and Welsch , R. 1977 . Robust Regression Using Iteratively Reweighted Least Squares . Communications in Statistics, Part A–Theory and Methods , 6 : 813 – 828 .
   Web of Science ®Google Scholar
• Huber , P. J. 1973 . Robust Regression: Asymptotics, Conjectures, and Monte Carlo . The Annals of Statistics , 1 : 799 – 821 .
   Web of Science ®Google Scholar
• Jorgensen , M. A. 1987 . Jackknifing Fixed Points of Iterations . Biometrika , 74 : 207 – 211 .
   Web of Science ®Google Scholar
• Jorgensen , M. A. 1990 . Influence Functions for Iteratively Defined Statistics: Applications to Iteratively Reweighted Least Squares , University of Waterloo, Dept. of Statistics . Technical Report 90–25
   Google Scholar
• Jurečkova , J. and Portnoy , S. 1987 . Asymptotics for One-Step M-Estimators in Regression With Application to Combining Efficiency and High Breakdown Point . Communications in Statistics, Part A–Theory and Methods , 16 : 2187 – 2199 .
   Web of Science ®Google Scholar
• Koenker , R. and Bassett , G. 1978 . Regression Quantiles . Econometrica , 46 : 33 – 50 .
   Web of Science ®Google Scholar
• Luenberger , D. G. 1969 . Optimization by Vector Space Methods , New York : John Wiley .
   Google Scholar
• Ruppert , D. and Carroll , R. J. 1980 . Trimmed Least Squares Estimation in the Linear Model . Journal of the American Statistical Association , 75 : 828 – 838 .
   Web of Science ®Google Scholar
• Simpson , D. G. , Ruppert , D. and Carroll , R. J. 1989 . One-Step GM-Estimates for Regression With Bounded Influence and High Breakdown Point , Cornell University, School of Operations Research and Industrial Engineering . ORIE Technical Report
   Google Scholar
• Smyth , G. K. Curvature and Convergence . Proceedings of the Statistical Computing Section . pp. 278 – 283 . American Statistical Society .
   Google Scholar
• Smyth , G. K. 1989 . Generalized Linear Models With Varying Dispersion . Journal of the Royal Statistical Society , 51 : 47 – 60 . Ser. B
   Google Scholar
• Staudte , R. G. and Sheather , S. J. 1990 . Robust Estimation and Testing , New York : John Wiley .
   Google Scholar
• Welsch , R. E. Confidence Regions for Robust Regression . Proceedings of the Statistical Computing Section . pp. 36 – 42 . American Statistical Association .
   Google Scholar
• Welsh , A. 1987a . The Trimmed Mean in the Linear Model . The Annals of Statistics , 15 : 20 – 45 . (with discussion)
   Web of Science ®Google Scholar
• Welsh , A. 1987b . One-Step L-Estimators for the Linear Model . The Annals of Statistics , 15 : 626 – 641 .
   Web of Science ®Google Scholar