Robust regression estimators when there are tied values

Journal of Modern Applied Statistical Methods

Volumn 12, Issue 2, 2013, Pages 20-34

  Wilcox, Rand R ^a   Clark, Florence ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

Coakley Hettmansperger estimator; Harrell Davis estimator; MM estimator; Perceived control; Rank based regression; Theil Sen estimator; Tied values; Well Elderly II study

Indexed keywords

EID: 84897907593     PISSN: 15389472     EISSN: None     Source Type: Journal    
DOI: 10.22237/jmasm/1383278520     Document Type: Article

References (35)

1. Akritas, M. G., Murphy, S. A. & LaValley, M. P. (1995). The Theil-Sen estimator with doubly censored data and applications to astronomy. Journal of the American Statistical Association 90, 170-177.
2. Agostinelli, C. & Markatou, M. (1998). A one-step robust estimator for regression based on the weighted likelihood reweighting scheme. Statistics Probability Letters, 37, 341-350.
3. Chida, Y. & Steptoe, A. (2009). Cortisol awakening response and psychosocial factors: A systematic review and meta-analysis. Biological Psychology, 80, 265-278 .
4. Clow, A., Thorn, L., Evans, P. & Hucklebridge, F. (2004). The awakening cortisol response: Methodological issues and significance. Stress, 7, 29-37.
5. Coakley, C. W. & Hettmansperger, T. P. (1993). A bounded influence, high breakdown, efficient regression estimator. Journal of the American Statistical Association, 88, 872-880.
6. Dielman, T., Lowry, C. & Pfaffenberger, R. (1994). A comparison of quantile estimators. Communications in Statistics-Simulation and Computation, 23, 355-371.
7. Dietz, E. J. (1987). A comparison of robust estimators in simple linear regression. Communications in Statistics-Simulation and Computation, 16, 1209- 1227.
8. Dietz, E. J. (1989). Teaching regression in a nonparametric statistics course. American Statistician, 43, 35-40.
9. Eizenman, D. R., Nesselroade, J. R., Featherman, D. L. & Rowe, J. W. (1997). Intraindividual variability in perceived control in an older sample: The MacArthur successful aging studies. Psychology and Aging, 12, 489-502.
10. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. & Stahel, W. A. (1986). Robust Statistics. New York: Wiley.
11. Fernandes, R. & Leblanc, S. G. (2005). Parametric (modified least squares) and non-parametric (Theil-Sen) linear regressions for predicting biophysical parameters in the presence of measurement errors. Remote Sensing of Environment, 95, 303-316.
12. Harrell, F. E. & Davis, C. E. (1982). A new distribution-free quantile estimator. Biometrika, 69, 635-640.
13. Heritier, S., Cantoni, E, Copt, S. & Victoria-Feser, M.-P. (2009). Robust Methods in Biostatistics. New York: Wiley.
14. Hoaglin, D. C. (1985). Summarizing shape numerically: The g-and-h distribution. In D. Hoaglin, F. Mosteller & J. Tukey (Eds.) Exploring Data Tables Trends and Shapes. New York: Wiley, pp. 461-515.
15. Huber, P. J. & Ronchetti, E. (2009). Robust Statistics, 2nd Ed. New York: Wiley.
16. Jackson, J., Mandel, D., Blanchard, J., Carlson, M., Cherry, B., Azen, S., Chou, C.-P., Jordan-Marsh, M., Forman, T., White, B., Granger, D., Knight, B., & Clark, F. (2009). Confronting challenges in intervention research with ethnically diverse older adults: the USC Well Elderly II trial. Clinical Trials, 6, 90-101.
17. Jaeckel, L. A. (1972). Estimating regression coefficients by minimizing the dispersion of residuals. Annals of Mathematical Statistics, 43, 1449-1458.
18. Koenker, R. & Bassett, G. (1978). Regression quantiles. Econometrika, 46, 33-50.
19. Liu, R. G. & Singh, K. (1997). Notions of limiting P values based on data depth and bootstrap. Journal of the American Statistical Association, 92, 266-277.
20. Maronna, R. A., Martin, D. R. & Yohai, V. J. (2006). Robust Statistics: Theory and Methods. New York: Wiley.
21. Parrish, R. S. (1990). Comparison of quantile estimators in normal sampling. Biometrics, 46, 247-257.
22. Peng, H., Wang, S. & Wang, X. (2008).Consistency and asymptotic distribution of the Theil- Sen estimator. Journal of Statistical Planning and Inference, 138, 1836-1850.
23. Racine, J. & MacKinnon, J. G. (2007). Simulation-based tests than can use any number of simulations. Communications in Statistics-Simulation and Computation, 36, 357-365.
24. Rousseeuw, P. J. (1984). Least median of squares regression. Journal of the American Statistical Association, 79, 871-880.
25. Sen, P. K. (1968). Estimate of the regression coefficient based on Kendall's tau. Journal of the American Statistical Association, 63, 1379-1389.
26. Sfakianakis, M. E. & Verginis, D. G. (2006). A new family of nonparametric quantile estimators. Communications in Statistics-Simulation and Computation, 37, 337-345.
27. Sheather, S. J. & Marron, J. S. (1990). Kernel quantile estimators. Journal of the American Statistical Association, 85, 410-416.
28. Staudte, R. G. & Sheather, S. J. (1990). Robust Estimation and Testing. New York: Wiley.
29. Theil, H. (1950). A rank-invariant method of linear and polynomial regression analysis. Indagationes Mathematicae, 12, 85-91.
30. Wang, X. Q. (2005). Asymptotics of the Theil-Sen estimator in simple linear regression models with a random covariate. Nonparametric Statistics 17, 107-120.
31. Wilcox, R. R. (1998). Simulation results on extensions of the Theil-Sen regression estimator. Communications in Statistics-Simulation and Computation, 27, 1117-1126.
32. Wilcox, R. R. (2012a). Modern Statistics for the Social and Behavioral Sciences: A Practical Introduction. New York: Chapman Hall/CRC press.
33. Wilcox, R. R. (2012b). Introduction to Robust Estimation and Hypothesis Testing, 3rd Edition. San Diego, CA: Academic Press.
34. Wilcox, R. R., Erceg-Hurn, D., Clark, F. Carlson, M. (2013). Comparing two independent groups via the lower and upper quantiles. Journal of Statistical Computation and Simulation. DOI: 10.1080/00949655.2012.754026
35. Yohai, V. J. (1987). High breakdown point and high efficiency robust estimates for regression. Annals of Statistics, 15, 642-656.