Constrained estimation and likelihood intervals for censored data

Canadian Journal of Statistics

Volumn 33, Issue 1, 2005, Pages 71-83

  Vandal, Alain C ^a   Gentleman, Robert ^b   Liu, Xuecheng ^a  

^a MCGILL UNIVERSITY   (Canada)

^b DANA FARBER CANCER INSTITUTE   (United States)

Author keywords

Constrained estimation; Current status data; EM algorithm; Interval censored data; Interval estimation; Nonparametric maximum likelihood; Vertex exchange method

Indexed keywords

EID: 18444399294     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.1002/cjs.5540330106     Document Type: Article

References (24)

1. M. Banerjee & J. A. Wellner (2001). Likelihood ratio tests for monotone functions. The Annals of Statistics, 29, 1699-1731.
2. D. Böhning (1985). Numerical estimation of a probability measure. Journal of Statistical Planning and Inference, 11, 57-69.
3. D. Böhning, P. Schlattmann & E. Dietz (1996). Interval censored data: A note on the nonparametric maximum likelihood estimator of the distribution function. Biometrika, 83, 462-466.
4. A. P. Dempster, N. M. Laird & D. B. Rubin (1977). Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society Series B, 39, 1-38.
5. D. M. Finkelstein & R. A. Wolfe (1985). A semiparametric model for regression analysis of interval-censored failure time data. Biometrics, 41, 933-945.
6. R. Gentleman & C. J. Geyer (1994). Maximum likelihood for interval censored data: Consistency and computation. Biometrika, 81, 618-623.
7. R. Gentleman & A. C. Vandal (2001). Computational algorithms for censored data using intersection graphs. Journal of Computational and Graphical Statistics, 10, 403-421.
8. R. Gentleman & A. C. Vandal (2002). Graph-theoretical aspects of bivariate censored data. The Canadian Journal of Statistics, 30, 557-571.
9. P. E. Gill, W. Murray & M. H. Wright (1981). Practical Optimization. Academic Press, London.
10. O. Kallenberg (1983). Random Measures, 3rd edition. Akademie-Verlag, Berlin.
11. D. K. Kim & J. M. G. Taylor (1995). The restricted EM algorithm for maximum likelihood estimation under linear restrictions on the parameters. Journal of the American Statistical Association, 90, 708-716.
12. M. L. Lesperance & J. D. Kalbfleisch (1992). An algorithm for computing the nonparametric MLE of a mixing distribution. Journal of the American Statistical Association, 87, 120-126.
13. B. G. Lindsay (1995). Mixture Models: Theory, Geometry, and Applications. NSF-CBMS Regional Conference Series in Probability and Statistics 5, Institute of Mathematical Statistics & American Statistical Association.
14. S. A. Murphy (1995). Likelihood ratio-based confidence intervals in survival analysis. Journal of the American Statistical Association, 90, 1399-1405.
15. A. B. Owen (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika, 75, 237-249.
16. R. M. Royall (1999). Statistical Evidence: A Likelihood Paradigm. Chapman & Hall, London.
17. E. Susko, J. D. Kalbfleisch & J. Chen (1998). Constrained nonparametric maximum-likelihood estimation for mixture models. The Canadian Journal of Statistics, 26, 601-617.
18. D. R. Thomas & G. L. Grunkemeier (1975). Confidence interval estimation of survival probabilities for censored data. Journal of the American Statistical Association, 70, 865-871.
19. B. W. Turnbull (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data. Journal of the Royal Statistical Society Series B, 38, 290-295.
20. C. Vaillancourt, I. Shrier, A. Vandal, M. Falk, M. Rossignol, A. Vernec & D. Somogyi (2004). Acute compartment syndrome: how long before muscle necrosis occurs? Canadian Journal of Emergency Medicine, 6, 147-154.
21. A. C. Vandal (1999). Order Theory and Nonparametric Analysis for Interval Censored Data. Doctoral dissertation, University of Auckland, New Zealand.
22. C.-F. J. Wu (1978). Some algorithmic aspects of the theory of optimal designs. The Annals of Statistics, 6, 1286-1301.
23. C.-F. J. Wu (1983). On the convergence properties of the EM algorithm. The Annals of Statististics, 11, 95-103.
24. Q. Yu, A. Schick, L. Li & G. Y. C. Wong (1998). Asymptotic properties of the GMLE with case 2 interval-censored data. Statistics & Probability Letters, 37, 223-228.