Finite sample stability properties of the least median of squares estimator

Journal of Statistical Computation and Simulation

Volumn 58, Issue 4, 1997, Pages 371-383

  Sheather, Simon J ^a   McKean, Joseph W ^b   Hettmansperger, Thomas P ^c  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b WESTERN MICHIGAN UNIVERSITY   (United States)

^c PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Breakdown point; Curse of dimensionality; Exact fit; Influence function; Linear model; LMS estimate; Robustness; Sensitivity curve

Indexed keywords

EID: 0040052323     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659708811841     Document Type: Article

References (12)

1. Coakley, C. W. and Hettmansperger, T. P. (1993) "A Bounded Influence, High Breakdown, Efficient Regression Estimator," The Journal of the American Statistical Association, 88, 872-880.
2. Croux, C., Rousseeuw, P. J. and Hossjer, O. (1994) "Generalized S-Estimators," The Journal of the American Statistical Association, 89, 1271-81.
3. Davies, P. L. (1993) "Aspects of Robust Linear Regression," The Annals of Statistics, 21, 1843-99.
4. Hampel, F. R. (1975) "Beyond Location Parameters: Robust Concepts and Methods," Bull. Int. Stat. Inst., 46, 375-82.
5. Hettmansperger, T. P. and Sheather, S. J. (1992) "A cautionary note on the method of least median squares", The American Statistician, 46, 79-83.
6. Hettmansperger, T. P. and Sheather, S. J. (1993) Reply to Comment by Appa and Land on "A cautionary note on the method of least median squares", The American Statistician, 47, 161-162.
7. Rousseeuw, P. J. (1984) "Least Median Squares Regression," The Journal of the American Statistical Association, 79, 871-880.
8. Rousseeuw, P. J. (1994) "Unconventional Features of Positive-Breakdown Estimators," Statistics and Probability Letters, 19, 417-31.
9. Rousseeuw, P. J. and LeRoy, A. M. (1987) Robust Regression and Outlier Detection, New York: John Wiley and Sons.
10. Rousseeuw, P. J. and van Zomeren, B C. (1990) "Unmasking multivanate outliers and leverage points," The Journal of the American Statistical Association, 85, 633-639.
11. Simpson, D. G., Ruppert, D. and Carroll, R. J. (1992) "On One-Step GM Estimates and Stability of Inference in Linear Regression,'' The Journal of the American Statistical Association, 87, 439-450.
12. Stromberg, A. J. (1993) "Computing the exact least median of squares estimate and stability diagnostics in multiple linear regression," SIAM Journal of Scientific Computing, 14, 1289-1299.