Robust Nonparametric Methods

Journal of the American Statistical Association

Volumn 95, Issue 452, 2000, Pages 1308-1312

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

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b WESTERN MICHIGAN UNIVERSITY   (United States)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0442277952     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2000.10474337     Document Type: Article

References (42)

1. Ammann, L. P. (1993), “Robust Singular Value Decompositions: A New Approach to Projection Pursuit,” Journal of the American Statistical Association, 88, 505-514.
2. Carroll, R. J., Ruppert, D., and Stefanski, L. A. (1999), Comment on “Regression Depth,” Journal of the American Statistical Association, 94, 410-411.
3. Chang, W. H., McKean, J. W., Naranjo, J. D., and Sheather, S. J. (1999), “High-Breakdown Rank Regression,” Journal of the American Statistical Association, 94, 205-219.
4. Chernoff, H., and Savage, I. R. (1958), “Asymptotic Normality and Efficiency of Certain Nonparametric Test Statistics,” Annals of Mathematical Statistics, 39, 972-994.
5. Cook, R. D. (1998), Regression Graphs., New York: Wiley.
6. Cook, R. D., and Nachsteim, C. J. (1994), “Reweighting to Achieve El-liptically Contoured Covariates in Regression,” Journal of the American Statistical Association, 89, 592-600.
7. Cook, R. D., Hawkins, D. M., and Weisberg, S. (1992), “Comparison of Model Misspecification Diagnostics Using Residuals From Least Mean of Squares and Least Median of Squares Fits,” Journal of the American Statistical Association, 87, 419-424.
8. Croux, C., Rousseeuw, P. J., and Hössjer, O. (1994), “Generalized S-Estimators,” Journal of the American Statistical Association, 89, 1271-1281.
9. Davies, P. L. (1993), “Aspects of Robust Linear Regression,” The Annals of Statistics, 21, 1843-1899.
10. Ellis, S. P. (1998), “Instability of Least Squares, Least Absolute Deviation, and Least Median of Squares Linear Regression,” Statistical Science, 13, 337-350.
11. Duan, N and Li, K. C. (1991), “Slicing Regression: A Link-Free Regression Method,” The Annals of Statistics, 19, 505-530.
12. Hâjek, J., and Šidak, Z. (1967), Theory of Rank Tests, New York: Academic Press.
13. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. J. (1986), Robust Statistics, the Approach Based on Influence Functions, New York: Wiley.
14. Hettmansperger, T. P. (1984), Statistical Inference Based on Ranks, New York: Wiley.
15. Hettmansperger, T. P., and McKean, J. W. (1983), “A Geometric Interpretation of Inferences Based on Ranks in the Linear Model,” Journal of the American Statistical Association, 78, 885-893.
16. Hettmansperger, T. P., and McKean, J. W. (1998), Robust Nonparametric Statistical Methods, London: Arnold.
17. Hettmansperger, T. P., and Sheather, S. J. (1992), “A Cautionary Note on the Method of Least Median Squares,” The American Statistician, 46, 79-83.
18. Jaeckel, L. A. (1972), “Estimating Regression Coefficients by Minimizing the Dispersion of Residuals,” The Annals of Mathematical Statistics, 43, 1449-1458.
19. Jureckova, J. (1971), “Nonparametric Estimate of Regression Coefficients,” The Annals of Mathematical Statistics, 42, 1328-1338.
20. Krasker, W. S., and Welsch, R. E. (1982), “Efficient Bounded Influence Regression Estimation,” Journal of the American Statistical Association, 77, 595-604.
21. Koul, H. L. (1992), Weighted Empiricals and Linear Models, Hayward, CA: Institute of Mathematical Statistics.
22. Lehmann, E. L. (1975), Nonparametrics: Statistical Methods Based on Ranks, San Francisco: Holden-Day.
23. McKean, J. W., Naranjo, J. D., and Sheather, S. J. (1996), “Diagnostics to Detect Differences in Robust Fits of Linear Models,” Computational Statistics, 11, 223-243.
24. McKean, J. W., and Schrader, R. (1980), “The Geometry of Robust Procedures in Linear Models,” Journal of the Royal Statistical Society, Ser. B, 42, 366-371.
25. McKean, J. W., and Sheather, S. J. (1991), “Small-Sample Properties of Robust Analyses of Linear Models Based on R-Estimates,” in A Survey in Directions in Robust Statistics and Diagnostics, Part II, eds. W. Stahel and S. Weisberg, New York: Springer-Verlag, pp. 1-20.
26. McKean, J. W., Sheather, S. J., and Hettmansperger, T. P. (1990), “Regression Diagnostics for Rank-Based Methods,” Journal of the American Statistical Association, 85, 1018-28.
27. McKean, J. W., Sheather, S. J., and Hettmansperger, T. P. (1993), “The Use and Interpretation of Residuals Based on Robust Estimation,” Journal of the American Statistical Association, 88, 1254-1263.
28. McKean, J. W., Sheather, S. J., and Hettmansperger, T. P. (1994), “Robust and High-Breakdown Fits of Polynomial Models,” Technometrics, 36, 409-415.
29. Naranjo, J. D., and Hettmansperger, T. P. (1994), “Bounded-Influence Rank Regression,” Journal of the Royal Statistical Society, Ser. B, 56, 209-220.
30. Puri, M. L., and Sen, P. K. (1971), Nonparametric Methods in Multivariate Analysis, New York: Wiley.
31. Puri, M. L., and Sen, P. K. (1985), Nonparametric Methods in General Linear Models, New York: Wiley.
32. Randles, R. H., and Wolfe, D. A. (1979), Introduction to the Theory of Nonparametric Statistics, New York: Wiley.
33. Rousseeuw, P., Hubert, M., and Van Aelst, S. (1999), “Reply to Comments: Regression Depth,” Journal of the American Statistical Association.
34. Rousseeuw, P. J., and Leroy, A. M. (1987), Robust Regression and Outlier Detection, New York: Wiley.
35. Rousseeuw, P., and Van Driessen, K. (1998), “A Fast Algorithm for the Minimum Covariance Determinant Estimator,” technical report, University of Antwerp.
36. Rousseeuw, P., and Van Driessen, K. (1999), “Computing LTS Regression for Large Data Sets,” technical report, University of Antwerp.
37. Rousseeuw, P. J., and Yohai, V. J. (1984), “Robust Regression by Means of S-Estimators,” in Robust and Nonlinear Time Series, eds. J. Franke, W. Hardie, and R. D. Martin, New York: Springer-Verlag, pp. 256-272.
38. Rubun, D. B., and Thomas, N. (1996), “Matching Using Estimated Propensity Scores: Relating Theory to Practice,” Biometrics, 52, 254-268.
39. Sheather, S. J., McKean, J. W., and Hettmansperger, T. P. (1997), “Finite Sample Stability Properties of the Least Median of Squares Estimator,” Journal of Statistical Computation and Simulation, 58, 371-383.
40. Simpson, D. G., and Chang, Y. I. (1997), “Reweighting Approximate GM Estimators: Asymptotics and Residual-Based Graphics,” Journal of Statistical Planning and Inference, 57, 273-293.
41. Simpson, D. G., Ruppert, D., and Carroll, R. J. (1992), “On One-Step GM Estimates and Stability of Inferences in Linear Regression,” Journal of the American Statistical Association, 87, 439-450.
42. Simpson, D. G., and Yohai, V. J. (1998), “Functional Stability of One-Step GM Estimators in Approximately Linear Regression,” The Annals of Statistics, 26, 1147-1169.