Singly and doubly censored current status data: Estimation, asymptotics and regression

Scandinavian Journal of Statistics

Volumn 24, Issue 3, 1997, Pages 289-307

  Van Der Laan, Mark J ^a   Bickel, Peter J ^a   Jewell, Nicholas P ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Efficient influence curve; Location parameter; Regularized maximum likelihood estimator

Indexed keywords

EID: 0031476490     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.t01-1-00064     Document Type: Article

References (25)

1. Ayer, M., Brunk, H. D., Ewing, G. M., Reid, W. T. & Silverman, E. (1955). An empirical distribution function for sampling with incomplete information. Ann. Statist. 26, 641-647.
2. Barlow, R. E., Bartholomew, D. J., Bremner, J. M. & Brunk, H. D. (1972). Statistical inference under order restrictions. Wiley, New York.
3. Bickel, P. J., Klaassen, C. A. J., Ritov, Y. & Wellner, J. A. (1993). Efficient and adaptive inference in semiparametric models. Johns Hopkins University Press, Baltimore.
4. Diamond, I. D., McDonald, J. W. & Shah, I. H. (1986). Proportional hazards models for current status data: application to the study of differentials in age at weaning in Pakistan. Demography 23, 607-620.
5. Diamond, I. D. & McDonald, J. W. (1991). The analysis of current status data. Demographic applications of event history analysis, (eds J. Trussell, R. Hankinson & J. Tilton), Oxford University Press, Oxford.
6. Groeneboom, P. (1991) Nonparametric maximum likelihood estimators for interval censoring and deconvolution, Technical Report N. 378, Department of Statistics, Stanford University, California.
7. Groeneboom, P. & Wellner, J. A. (1992). Information bounds and nonparametric maximum likelihood estimation. Birkhäuser, Boston.
8. Huang, J. & Wellner, J. A. (1995). Asymptotic normality of the NPMLE of linear functionals for interval censored data, case I. Statist. Neerland. 49, 153-163.
9. Hoffmann-Jørgensen, J. (1984). Stochastic processes on Polish Spaces, Unpublished manuscript.
10. Huber, P. J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. Proc. Fifth Berk. Symp. Math. Statist. Probab. 1, 221-233. University of California Press, Berkeley.
11. Jewell, N. P. & Shiboski, S. C. (1990). Statistical analysis of HIV infectivity based on partner studies. Biometrics 46, 1133-1150.
12. Jewell, N. P., Malani, H. M. & Vittinghoff, E. (1994). Nonparametric estimation for a form of doubly censored data with application to two problems in aids, J. Amer. Statist. Assoc. 89, 7-18.
13. Keiding, K. (1991). Age-specific incidence and prevalence (with discussion). J. Roy. Statist. Soc. Ser. A 154, 371-412.
14. Rabinowitz, D., Tsiatis, A. & Aregon, J. (1995). Regression with interval censored data. Biometrika 82, 501-514.
15. Rabinowitz, D. & Jewell, N. P. (1996). Regression with doubly censored current status data. J. Roy. Statist. Soc. Sci. B 58, 541-550.
16. Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman & Hall, London.
17. Stone, C. (1980). Optimal rates of convergence for nonparametric estimators. Ann. Math. Statist. 8, 1348-1360.
18. van de Geer, S. (1993). Hellinger-consistency of certain nonparametric maximum likelihood estimators. Ann. Statist. 21, 14-44.
19. van de Geer, S. (1994). Asymptotic normality in mixture models. Preprint, University of Leiden, The Netherlands.
20. van der Laan, M. J. (1993). General identity for linear parameters in convex models with application to efficiency of the (NP)MLE. Preprint 765, Department of Mathematics, Utrecht, The Netherlands.
21. van der Laan, M. J. (1994a). Modified EM-estimator of the bivariate survival function, Math. Meth. Statist. 3, 213-243.
22. van der Laan, M. J. (1994b). Proving efficiency of NPMLE and identities. Technical Report N. 44, Group in Biostatistics, University of California, Berkeley.
23. van der Laan, M. J. (1996). Efficient and inefficient estimation in semiparametric models. CW1-tract # 114, Centre for Mathematics and Computer Science.
24. van der Vaart, A. W. (1991). Efficiency and Hadamard differentiable functional Scand. J. Statist. 18, 63-75.
25. van der Vaart, A. W. & Wellner, J. A. (1996). Weak convergence and empirical processes, Springer Verlag, New York.