Empirical likelihood confidence regions for comparison distributions and ROC curves

Canadian Journal of Statistics

Volumn 31, Issue 2, 2003, Pages 173-190

  Claeskens, Gerda ^a   Jing, Bing Yi ^b   Peng, Liang ^c   Zhou, Wang ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Bootstrap; Comparison distribution; Confidence region; Coverage accuracy; Empirical likelihood; ROC curve; Smoothing

Indexed keywords

EID: 0242679727     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3316066     Document Type: Article

References (33)

1. S. Chakraborti & R. Mukerjee (1989). A confidence interval for a measure associated with the comparison of a treatment with a control. South African Statistical Journal, 23, 219-230.
2. S. Chen & P. Hall (1993). Smoothed empirical likelihood confidence intervals for quantiles. The Annals of Statistics, 21, 1166-1181.
3. T. J. DiCiccio, P. Hall & J. P. Romano (1991). Empirical likelihood is Bartlett-correctable. The Annals of Statistics, 19, 1053-1061.
4. J. H. J. Einmahl & I. W. McKeague (1999). Confidence tubes for multiple quantile plots via empirical likelihood. The Annals of Statistics, 27, 1348-1367.
5. M. J. Goddard & I. Hinberg (1990). Receiver operating characteristic (ROC) curves and non normal data: an empirical study. Statistics in Medicine, 9, 325-337.
6. P. Hall (1979). On the rate of convergence of normal extremes. Journal of Applied Probability, 16, 433-439.
7. P. Hall & B. La Scala (1990). Methodology and algorithms of empirical likelihood. International Statistical Review, 58, 109-127.
8. P. Hall & A. B. Owen (1993). Empirical likelihood confidence bands in density estimation. Journal of Computational and Graphical Statistics, 2, 273-289.
9. J. A. Hanley & B. J. McNeil (1982). The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143, 29-36.
10. M. Hollander, I. W. McKeague & J. Yang (1997). Likelihood-ratio based confidence bands for survival functions. Journal of the American Statistical Association, 92, 215-226.
11. E. C. Holmgren (1995). The P-P plot as a method of comparing treatment effects. Journal of the American Statistical Association, 90, 360-365.
12. F. Hsieh & B. W. Turnbull (1996). Non-parametric and semi-parametric estimation of the receiver operating characteristic curve. The Annals of Statistics, 24, 25-40.
13. J. T. Kim (2000). An order selection criterion for testing goodness of fit. Journal of the American Statistical Association, 95, 829-835.
14. G. Li (1995). On nonparametric likelihood ratio estimation of survival probabilities for censored data. Statistics & Probability Letters, 25, 95-104.
15. G. Li, M. Hollander, I. W. McKeague & J. Yang (1996). Nonparametric likelihood ratio confidence bands for quantile functions from incomplete survival data. The Annals of Statistics, 24, 628-640.
16. G. Li, R. C. Tiwari & M. T. Wells (1996). Quantile comparison functions in two-sample problems, with applications to comparisons of diagnostic markers. Journal of the American Statistical Association, 91, 689-698.
17. G. Li, R. C. Tiwari & M. T. Wells (1999). Semiparametric inference for a quantile comparison function with applications to receiver operating characteristic curves. Biometrika, 86, 487-502.
18. C. J. Lloyd (1998). The use of smoothed ROC curves to summarize and compare diagnostic systems. Journal of the American Statistical Association, 93, 1356-1364.
19. C. J. Lloyd & Z. Yong (1999). Kernel estimators for the ROC curve are better than empirical. Statistics & Probability Letters, 44, 221-228.
20. C. E. Metz, B. A. Herman & J.-H. Shen (1998). Maximum likelihood estimation of receiver operating characteristic (ROC) curves from continuously-distributed data. Statistics in Medicine, 17, 1033-1053.
21. S. A. Murphy (1995). Likelihood ratio-based confidence intervals in survival analysis. Journal of the American Statistical Association, 90, 1399-1405.
22. A. B. Owen (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika, 75, 237-249.
23. A. B. Owen (1990). Empirical likelihood ratio confidence regions. The Annals of Statistics, 18, 90-120.
24. A. B. Owen (2001). Empirical Likelihood. Chapman & Hall, Boca Raton, FL.
25. E. Parzen (1979). Nonparametric statistical data modeling. Journal of the American Statistical Association, 74, 105-131.
26. E. Parzen (1998). Statistical methods mining, two sample data analysis, comparison distributions, and quantile limit theorems. In Asymptotic Methods in Probability and Statistics: A Volume in Honour of Miklós Csörgo″(B. Szyszkowicz, ed.), North-Holland, Amsterdam, pp. 611-617.
27. M. S. Pepe (1997). A regression modelling framework for receiver operating characteristic curves in medical diagnostic testing. Biometrika, 84, 595-608.
28. J. Qin & J. F. Lawless (1994). Empirical likelihood and general estimating equations. The Annals of Statistics, 22, 300-325.
29. R. J. Serfling (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
30. I. A. Swets & R. M. Pickett (1982). Evaluation of Diagnostic Systems: Methods from Signal Detection Theory. Academic Press, New York.
31. A. N. Tosteston & C. B. Begg (1988). A general regression methodology for ROC curve estimation. Medical Decision Making, 8, 205-215.
32. S. Wieand, M. H. Gail, B. R. James & K. L. James (1989). A family of nonparametric statistics for comparing diagnostic markers with paired and unpaired data. Biometrika, 76, 585-592.
33. K. H. Zou, W. H. Hall & D. E. Shapiro (1997). Smooth non-parametric receiver operating characteristic (ROC) curves for continuous diagnostic tests. Statistics in Medicine, 16, 2143-2156.