Markov chain marginal bootstrap

Journal of the American Statistical Association

Volumn 97, Issue 459, 2002, Pages 783-795

  He, X ^a   Hu, F ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY OF VIRGINIA   (United States)

Author keywords

Asymptotic normality; Confidence interval; Generalized linear model; M estimator; Maximum likelihood; Regression

Indexed keywords

EID: 0036744531     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214502388618591     Document Type: Review

References (29)

1. Bai, Z.D., and He, X. (1999), "Asymptotic Distribution of the Maximal Depth Estimators for Regression and Multivariate Location," The Annals of Statistics, 27, 1616-1637.
2. Bai, Z.D., Rao, C.R., and Wu, Y. (1992), "M-Estimation of Multivariate Linear Regression Parameters Under a Convex Discrepancy Function," Statistica Sinica, 2, 237-254.
3. Chung, K.L. (1974), A Course in Probability Theory (2nd ed.), New York: Academic Press.
4. Diciccio, T.J., and Efron, B. (1996), "Bootstrap Confidence Intervals" (with discussion), Statistical Science, 11, 189-228.
5. Diciccio, T.J., and Romano, J.P. (1988), "A Review of Bootstrap Confidence Intervals," Journal of the Royal Statistical Society, Ser. B, 50, 338-354.
6. Efron, B. (1979), "Bootstrap Methods: Another Look at the Jackknife," The Annals of Statistics, 7, 1-26.
7. Efron, B., and Tibshirani, R.J. (1993), An Introduction to Bootstrap, New York: Chapman and Hall.
8. Freedman, D.A. (1981), "Bootstrapping Regression Models," The Annals of Statistics, 9, 1228-1228.
9. Godambe, V.P., and Kale, B.K. (1991), "Estimating Functions: An Overview," Estimating Functions (V.P. Godambe, ed.), Oxford University Press, Oxford, pp. 3-20.
10. Gutenbrunner, C., Jurečková, J., Koenker, R., and Portnoy, S. (1993), "Tests of Linear Hypotheses Based on Regression Rank Scores," Journal of Nonparametric Statistics, 2, 307-331.
11. Hall, P. (1992), The Bootstrap and Edgeworth Expansion, New York: Springer-Verlag. Berlin.
12. Hall, P., and Sheather, S.J. (1988), "On the Distribution of a Studentized Quantile," Journal of the Royal Statistical Society, Ser. B, 50, 381-391.
13. Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., and Stahel, W.A. (1986), Robust Statistics: The Approach Based on Influence Functions, New York: Wiley.
14. Hannan, E.J. (1970), Multiple Time Series. New York: Wiley.
15. He, X., and Shao, Q.M. (1996), "A General Bahadur Representation of M-Estimators and Its Application to Linear Regression With Nonstochastic Design," The Annals of Statistics, 24, 2608-2630.
16. Hosmer, D.W., and Lemeshow, S. (1989), Applied Logistic Regression, New York: Wiley.
17. Hu, F., and Kalbfleisch, J.D. (1997), "Estimating Equations and the Bootstrap," in Selected Proceedings of the Symposium on Estimating Equations, eds. I.V. Basawa, V.P. Godambe and R.L. Taylor, Hayward, CA: IMS, pp. 405-416.
18. _ (2000), "The Estimating Equation Bootstrap" (with discussion), Canadian Journal of Statistics, 28, 449-499.
19. Hu, F., and Zidek, J.V. (1995), "A Bootstrap Based on the Estimating Equations of the Linear Model," Biometrika, 82, 263-275.
20. Koenker, R. (1994), "Confidence Intervals for Regression Quantiles," in Asymptotic Statistics: Proceedings of the 5th Prague Symposium on Asymptotic Statistics, eds. P. Mandl and M. Huskova, Heidleberg: Physica-Verlag.
21. Lahiri, S.N. (1992), "Bootstrapping M-Estimators of a Multiple Linear Regression Parameter," The Annals of Statistics, 20, 1548-1570.
22. Liu, R.Y. (1988), "Bootstrap Procedures Under Some Non-iid Models," The Annals of Statistics, 16, 1696-1708.
23. McCullagh, P., and Nelder, J.A. (1989), Generalized Linear Models (2nd ed.), London: Chapman and Hall.
24. Parzen, M.I., Wei, L.J., and Ying, Z. (1994), "A Resampling Method Based on Pivotal Estimating Functions," Biometrika, 81, 341-350.
25. Petrov, V.V. (1995), Limit Theorems of Probability Theory-Sequences of Independent Random Variables, Oxford, U.K.: Oxford Science Publications.
26. Shao, J., and Tu, D. (1995), The Jackknife and Bootstrap, New York: Springer-Verlag. Berlin.
27. Searle, S.R. (1982), Matrix Algebra Useful for Statistics, New York: Wiley.
28. Yohai, V.J., and Maronna, R.A. (1979), "Asymptotic Behavior of M-Estimators for the Linear Model," The Annals of Statistics, 7, 258-268.
29. Zhou, Q., and Portnoy, S.L. (1996), "Direct Use of Regression Quantiles to Construct Confidence Sets in Linear Models," The Annals of Statistics, 24, 287-306.