Smoothed weighted empirical likelihood ratio confidence intervals for quantiles

Bernoulli

Volumn 14, Issue 3, 2008, Pages 725-748

  Ren, Jian Jian ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Bootstrap; Doubly censored data; Empirical likelihood; Interval censored data; Partly interval censored data; Right censored data

Indexed keywords

EID: 53349118443     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/08-BEJ129     Document Type: Article

References (47)

1. Banerjee, M. and Wellner, J.A. (2001). Likelihood ratio tests for monotone functions. Ann. Statist. 29 1699-1731.
2. Banerjee, M. and Wellner, J.A. (2005). Confidence intervals for current status data. Scand. J. Statist. 32 405-424.
3. Bickel, P.J., Götze, F. and van Zwet, W.R. (1997). Resampling fewer than n observations: Gains, losses, and remedies for losses. Statist. Sinica 7 1-31.
4. Bickel, P.J. and Ren, J. (1996). The m out of n bootstrap and goodness of fit tests with doubly censored data. Robust Statistics, Data Analysis, and Computer Intensive Methods (Schloss Thurnau, 1994). Lecture Notes in Statist. 109 35-47. New York: Springer.
5. Bickel, P.J. and Sakov, A. (2008). On the choice of m in the m out of n bootstrap and confidence bounds for extrema. Statist. Sinica 18 967-985.
6. Chang, M.N. and Yang, G.L. (1987). Strong consistency of a nonparametric estimator of the survival function with doubly censored data. Ann. Statist. 15 1536-1547.
7. Chen, S.X. and Hall, P. (1993). Smoothed empirical likelihood confidence intervals for quantiles. Ann. Statist. 21 1166-1181.
8. Chen, K. and Lo, S.-H. (1996). On bootstrap accuracy with censored data. Ann. Statist. 24 569-595.
9. Chen, K. and Zhou, M. (2003). Non-parametric hypothesis testing and confidence intervals with doubly censored data. Lifetime Data Anal. 9 71-91.
10. Chung, K.L. (1974). A Course in Probability Theory. New York: Academic Press.
11. DiCiccio, T.J., Hall, P.J. and Romano, J. (1991). Empirical likelihood is Bartlett-correctable. Ann. Statist. 19 1053-1061.
12. Efron, B. (1967). The two sample problem with censored data. Proc. Fifth Berkeley Symp. Math. Stat. Prob. 4 831-853. Berkeley: Univ. California Press.
13. Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Ann. Statist. 7 1-26.
14. Efron, B. and Tibshirani, R.J. (1993). An Introduction to the Bootstrap. New York: Chapman and Hall.
15. Enevoldsen, A.K., Borch-Johnson, K., Kreiner, S., Nerup, J. and Deckert, T. (1987). Declining incidence of persistent proteinuria in type I (insulin-dependent) diabetic patient in Denmark. Diabetes 36 205-209.
16. Gill, R.D. (1983). Large sample behavior of the product-limit estimator on the whole line. Ann. Statist. 11 49-58.
17. Götze, F. and Račkauskas, A. (2001) The Bootstrap in hypothesis testing. State of the Art in Statistics and Probability Theory. Festschrift for Willem R. van Zwet. IMS Lecture Notes in Mathematical Statistics 36 286-309. Beachwood, OH: IMS.
18. Groeneboom, P. and Wellner, J.A. (1992). Information Bounds and Nonparametric Maximum Likelihood Estimation. Basel: Birkhäuser.
19. Gu, M.G. and Zhang, C.H. (1993). Asymptotic properties of self-consistent estimators based on doubly censored data. Ann. Statist. 21 611-624.
20. Hall, P. (1992). The Bootstrap and Edgeworth Expansion. New York: Springer.
21. Huang, J. (1999). Asymptotic properties of nonparametric estimation based on partly interval-censored data. Statist. Sinica 9 501-519.
22. Kaplan, E.L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53 457-481.
23. Kim, M.Y., De Gruttola, V.G. and Lagakos, S.W. (1993). Analyzing doubly censored data with covariates, with application to AIDS. Biometrics 49 13-22.
24. Li, G., Hollander, M., McKeague, I.W. and Yang, J. (1996). Nonparametric likelihood ratio confidence bands for quantile functions from incomplete survival data. Ann. Statist. 24 628-640.
25. Miller, R.G. (1976). Least squared regression with censored data. Biometrika 63 449-464.
26. Mykland, P.A. (1995). Dual likelihood. Ann. Statist. 23 396-421.
27. Mykland, P.A. and Ren, J. (1996). Self-consistent and maximum likelihood estimation for doubly censored data. Ann. Statist. 24 1740-1764.
28. Odell, P.M., Anderson, K.M. and D'Agostino, R.B. (1992). Maximum likelihood estimation for interval censored data using a Weibull-based accelerated failure time model. Biometrics 48 951-959.
29. Owen, A.B. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75 237-249.
30. Owen, A.B. (1990). Empirical likelihood ratio confidence regions. Ann. Statist. 18 90-120.
31. Owen, A.B. (1991). Empirical likelihood for linear models. Ann. Statist. 19 1725-1747.
32. Owen, A.B. (2001). Empirical Likelihood. New York: Chapman and Hall.
33. Politis, D.N., Romano, J.P. and Wolf, M. (1999). Subsampling. New York: Springer.
34. Qin, J. and Lawless, J.F. (1994). Empirical likelihood and general estimating equations. Ann. Statist. 22 300-325.
35. Ren, J. (1995). Generalized Cramér-von Mises tests of goodness of fit with doubly censored data. Ann. Inst. Statist. Math. 47 525-549.
36. Ren, J. (1997). On self-consistent estimators and kernel density estimators with doubly censored data. J. Statist. Plann. Inference 64 27-43.
37. Ren, J. (2001). Weight empirical likelihood ratio confidence intervals for the mean with censored data. Ann. Inst. Statist. Math. 53 498-516.
38. Ren, J. (2003). Goodness of fit tests with interval censored data. Scand. J. Statist. 30 211-226.
39. Ren, J. (2006). The Lipschitz condition in the expansion of weighted empirical log-likelihood ratio. Internat. J. Statist. Manag. Syst. 1 1-23.
40. Ren, J. (2008). Weighted empirical likelihood in some two-sample semiparametric models with various types of censored data. Ann. Statist. 36 147-166.
41. Ren, J. and Peer, P.G. (2000). A study on effectiveness of screening mammograms. Internat J. Epidemiology 29 803-806.
42. Royden, H.L. (1968). Real Analysis. New York: MacMillan Publishing Co.
43. Shorack, G.R. and Wellner, J.A. (1986). Empirical Processes with Applications to Statistics. New York: Wiley.
44. Stute, W. and Wang, J.L. (1993). The strong law under random censorship. Ann. Statist. 21 1591-1607.
45. Turnbull, B.W. (1974). Nonparametric estimation of a survivorship function with doubly censored data. J. Amer. Statist. Assoc. 69 169-173.
46. Wellner, J.A. (1995). Interval censoring case 2: Alternative hypothesis. In Analysis of Censored Data 271-291. Hayward, CA: IMS.
47. Zhou, M. (2005). Empirical likelihood analysis of the rank estimator for the censored accelerated failure time model. Biometrika 92 492-498.