Estimation in the simple linear regression model when there is heteroscedasticity of unknown form

Communications in Statistics - Theory and Methods

Volumn 25, Issue 6, 1996, Pages 1305-1324

  Wilcox, Rand R ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

Bootstrap; M regression; Robust hypothesis testing; Smoother; Weighted least squares

Indexed keywords

EID: 0040116044     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1080/03610929608831766     Document Type: Article

References (22)

1. Beran, R. (1987). "Prepivoting to reduce level error of confidence," Biometrika, 54, 457-468.
2. Carroll, R. J. & Ruppcrt, D. (1982). "Robust estimation in heteroscedastic linear models," Annals of Statistics, .10, 429-441.
3. Carroll, R. J. & Ruppert, D. (1988). Transformation and Weighting in Regression, New York: Chapman and Hall.
4. Coakley, C. W. &: Hettmansperger, T. P. (1993). "A bounded influence, high breakdown, efficient regression estimator," Journal of the American Statistical Association, 88, 872-880.
5. Cohen, M., Dalai, S. R. & Tukey, J. W. (1993). "Robust, smoothly heterogeneous variance regression," Applied Statistics, 42, 339-353.
6. De Jongh, P. J., De Wet, T. & Welsh, A. H. (1988). "Mallows-type bounded-influence-regression trimmed means," Journal of the American Statistical Association, 83, 805-810.
7. Dorfman, A. H. (1991). "Sound confidence intervals in the heteroscedastic linear model through releveraging," Journal of the Royal Statistical Society, B, 53, 441-452.
8. Efron, B. & Tibshirani, R. J. (1993). An Introduction to the Bootstrap. New York: Chapman and Hall.
9. Hall, P. (1986). "On the number of bootstrap simulations required to construct a confidence interval," Annals of Statistics, 14, 1431-1452.
10. Hastie, T. J. & Tibshirani, R. J. (1990). Generalized Additive Models, New York: Chapman and Hall.
11. Hoaglin, D. C. (1985). "Summarizing shape numerically: The g-and-h distributions," in Exploring Data Tables Trends and Shapes. (D. Hoaglin, F. Mosteller and J. Tukey, Eds.). New York: Wiley.
12. Mak, T. K. (1992). "Estimation of parameters in heteroscedastic linear models," Journal of the Royal Statistical Society, B, 54, 649-655.
13. MacKinnon, J. G. & White, H. (1985). "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, 29, 305-325.
14. Maronna, R. & Morgenthaler, S. (1986). "Robust regression through robust covariances," Communcations in Statistics-Theory and Methods, 15, 1347-1365.
15. Montgomery, D. C. & Peck, E. A. (1992). Introduction to Linear Regression Analysis. New York: Wiley.
16. Nanayakkara, N. & Cressie, N. (1991). "Robustness to unequal scale and other departures from the classical linear model," Directions in Robust Statistics and Diagnostics, Part II, (W. Stahel and S. Weisberg, Eds.). New York: Springer-Verlag, 65-113.
17. Robinson, P. M. (1987). "Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form," Econometrica, 55, 875-891.
18. Wiens, D. P. (1992) "A note on the computation of robust, bounded influence estimates and test statistics in regression," Computational Statistics & Data Analysis, 13, 211-220.
19. Wilcox, R. R. (1995a). "A regression smoother for resistant measures of location and scale," British Journal of Mathematical and Statistical Psychology, 48, 189-201.
20. Wilcox, R. R. (1995b). "ANOVA: The practical importance of heteroscedastic methods, using trimmed means versus means, and designing simulation studies," British Journal of Mathematical and Statistical Psychology, 48, 99-114.
21. Wilcox, R. R. (in press). "Confidence intervals for the slope of a regression line when the error term has non-constant variance" Computational Statistics & Data Analysis.
22. Wu, C. F. J. (1986). "Jackknife, bootstrap, and other resampling methods in regression analysis," Annals of Statistics, 14, 1261-1295.