Strong consistency of presmoothed Kaplan-Meier integrals when covariables are present

Statistics

Volumn 38, Issue 6, 2004, Pages 483-496

  De Uña Álvarez, Jacobo ^a   Rodríguez Campos, M Celia ^a  

^a UNIVERSITY OF VIGO   (Spain)

Author keywords

Censoring; Covariates; Martingales; Presmoothing

Indexed keywords

EID: 10244255218     PISSN: 02331888     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331880412331316065     Document Type: Article

References (21)

1. Andersen, P. K., Borgan, O., Gill, R. D. and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer, New York.
2. Cao, R., López de Ulibarri, I., Janssen, P. and Veraverbeke, N. (2003). Presmoothed Kaplan-Meier and Nelson-Aalen estimators. Technical Report 03-01, University of Santiago de Compostela, Spain.
3. Devroye, L. P. (1978a). The uniform convergence of nearest neighbor regression function estimators and their application in optimization. IEEE Transactions on Information Theory, 24, 142-151.
4. Devroye, L. P. (1978b). The uniform convergence of the Nadaraya-Watson regression function estimate. Canadian Journal of Statistics, 6, 179-191.
5. Dikta, G. (1998). On semiparametric random censorship models. Journal of Statistical Planning and Inference, 66, 253-279.
6. Dikta, G. (2000). The strong law under semiparametric random censorship models. Journal of Statistical Planning and Inference, 83, 1-10.
7. Dikta, G., Hansmann, R. and Schmidt, C. (2002). Some simulation results under random censorship models. InterStat manuscript March #1.
8. Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis. Wiley, New York.
9. Härdie, W. and Luckhaus, S. (1984). Uniform consistency of a class of regression function estimators. Annals of Statistics, 12, 612-623.
10. Hosmer, D. W. and Lemeshow, S. (1989). Applied Logistic Regression. Wiley, New York.
11. Kaplan, E. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457-481.
12. Mack, Y. P. and Silverman, B. W. (1982). Weak and strong uniform consistency of kernel regression estimates. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 61, 405-415.
13. Neveu, J. (1975). Discrete-Parameter Martingales. North-Holland, Amsterdam/Oxford.
14. Schimek, M. G. (2000). Smoothing and Regression. Approaches, Computation, and Application. Wiley, New York.
15. Stute, W. (1992). Strong consistency under the Koziol-Green model. Statistics & Probability Letters, 14, 313-320.
16. Stute, W. (1993). Consistent estimation under random censorship when covariables are present. Journal of Multiviriate Analysis, 45, 89-103.
17. Stute, W. (1996). Distributional convergence under random censorship when covariables are present. Scandinavian Journal of Statistics, 23, 461-471.
18. Stute, W. (1999). Nonlinear censored regression. Statistica Sinica, 9, 1089-1102.
19. Stute, W. and Wang, J.-L. (1993). The strong law under random censorship. Annals of Statistics, 21, 1591-1607.
20. de Uña-Álvarez, J. and González-Manteiga, W. (1999). Strong consistency under proportional censorship when covariables are present. Statistics & Probability Letters, 42, 283-292.
21. Ziegler, S. (1995). Ein Modifizierter Kaplan-Meier Schätzer. Diplomarbeit, Matematisches Institut, Justus-Liebig-Universitat, Gießen.