Maximum smoothed likelihood estimation and smoothed maximum likelihood estimation in the current status model

Annals of Statistics

Volumn 38, Issue 1, 2010, Pages 352-387

  Geurtboom, Piet ^a   Jongbloed, Geurt ^a   Witte, Birgit I ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Asymptotic distribution; Current status data; Density estimation; Distribution estimation; Hazard rate estimation; Maximum smoothed likelihood; Smoothed maximum likelihood

Indexed keywords

EID: 73949129777     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-AOS721     Document Type: Article

References (24)

1. BICKEL, P. J. and FAN, J. (1996). Some problems on the estimation of unimodal densities. Statist. Sinica 6 23-45. MR1379047 (Pubitemid 126706297)
2. DONOHO, D. L. and JOHNSTONE, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90 1200-1224. MR1379464
3. DÜMBGEN, L., FREITAG-WOLF, S. and JONGBLOED, G. (2006). Estimating a unimodal distribution function from interval censored data. J. Amer. Statist. Assoc. 101 1094-1106. MR2324149
4. DÜMBGEN, L. and RUFIBACH, K. (2009).Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency. Bernoulli 15 40-68.
5. EFRON, B. (1979). Bootstrap methods: Another look at the jackknife. Ann. Statist. 7 1-26. MR0515681
6. EGGERMONT, P. P. B. and LARICCIA, V. N. (2001). Maximum Penalized Likelihood Estimation. Springer, New York. MR1837879
7. GONZÁLEZ-MANTEIGA, W., CAO, R. and MARRON, J. S. (1996). Bootstrap selection of the smoothing parameter in nonparametric hazard rate estimation. J. Amer. Statist. Assoc. 91 1130-1140. MR1424613
8. GROENEBOOM, P., JONGBLOED, G. and WELLNER, J. A. (2002). A canonical process for estimation of convex functions: The invelope of integrated brownian motion +t4. Ann. Statist. 29 1620-1652. MR1891741
9. GROENEBOOM, P. andWELLNER, J. A. (1992). Information Bounds and Nonparametric Maximum Likelihood Estimation. Cambridge Univ. Press, New York. MR1180321
10. HAZELTON, M. L. (1996). Bandwidth selection for local density estimators. Scand. J. Statist. 23 221-232. MR1394655
11. HUANG, Y. and ZHANG, C. H. (1994). Estimating a monotone density from censored observations. Ann. Statist. 22 1256-1274. MR1311975
12. JONES, M. C. (1993). Simple boundary correction for kernel density estimation. Stat. Comput. 3 135-146.
13. KAPLAN, E. L. and MEIER, P. (1958). Nonparametric estimation from incomplete data. J. Amer. Statist. Assoc. 53 457-481. MR0093867
14. KEIDING, N. (1991). Age-specific incidence and prevalence: A statistical perspective. J. Roy. Statist. Soc. Ser. A 154 371-412. MR1144166
15. MAMMEN, E. (1991). Estimating a monotone regression function. Ann. Statist. 19 724-740. MR1105841
16. MARRON, J. S. and PADGETT, W. J. (1987). Asymptotically optimal bandwidth selection for kernel density estimators from randomly right-censored samples. Ann. Statist. 15 1520-1535. MR0913571
17. PATIL, P. N.,WELLS, M. T. andMARRON, J. S. (1994). Some heuristics of kernel based estimators of ratio functions. J. Nonparametr. Stat. 4 203-209. MR1290930
18. SCHUSTER, E. F. (1985). Incorporating support constraints into nonparametric estimators of densities. Comm. Statist. Theory Methods 14 1123-1136. MR0797636
19. SHEATHER, S. J. (1983). A data-based algorithm for choosing the window width when estimating the density at a point. Comput. Statist. Data Anal. 1 229-238.
20. SILVERMAN, B. W. (1978).Weak and strong uniform consistency of the kernel estimate of a density and its derivative. Ann. Statist. 6 177-184. MR0471166
21. SILVERMAN, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London. MR0848134
22. VAN DE GEER, S. A. (2000). Applications of Empirical Process Theory. Cambridge Univ. Press, New York. MR1739079
23. VAN DER VAART, A. W. and VAN DER LAAN, M. J. (2003). Smooth estimation of a monotone density. Statistics 37 189-203. MR1986176
24. VAN DER VAART, A.W. andWELLNER, J. A. (1996). Weak Convergence and Empirical Processes. Springer, New York. MR1385671