Estimating a distribution function for censored time series data

Journal of Multivariate Analysis

Volumn 78, Issue 2, 2001, Pages 299-318

  Cai, Zongwu ^a  

^a UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

censored data; consistency; Kaplan Meier estimator; time series analysis; variance estimator; weak convergence; mixing

Indexed keywords

EID: 0035429591     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.2000.1953     Document Type: Article

References (35)

1. Andrews D. W. K. Laws of large numbers for dependent nonidentically distributed random variables. Econ. Theory. 4:1988;458-467.
2. Auestad B., Tjøstheim D. Identification of nonlinear time series: First order characterization and order determination. Biometrika. 77:1990;669-687.
3. Billingsley P. Convergence of Probability Measures. 1968;Wiley, New York.
4. Breslow N., Crowley J. A large sample study of the life table and product limit estimators under random censorship. Ann. Statist. 2:1974;437-453.
5. Cai Z. Asymptotic properties of Kaplan-Meier estimator for censored dependent data. Statist. Probab. Lett. 37:1998;381-389.
6. Cai J., Prentice R. L. Estimating equations for hazard ratio parameters based on correlated failure time data. Biometrika. 82:1995;151-164.
7. Cai Z., Roussas G. G. Uniform strong estimation under α-mixing, with rates. Statist. Probab. Lett. 15:1992;47-55.
8. Cai Z., Roussas G. G. Kaplan-Meier estimator under association. J. Multivariate Anal. 67:1998;318-348.
9. Chen R., Tsay R. Functional coefficient autoregressive models. J. Amer. Statist. Assoc. 88:1993;298-308.
10. Cox R. D., Oakes D. Analysis of Survival Data. 1984;Chapman and Hall, London.
11. Gill R. D. Censoring and Stochastic Integrals. Mathematical Centre Tracts. 124:1980;Mathematisch Centrum, Amsterdam.
12. Gill R. D. Testing with replacement and the product limit estimator. Ann. Statist. 9:1981;853-860.
13. Gill R. D. Large sample behavior of the product limit estimator on the whole line. Ann. Statist. 11:1983;49-56.
14. Gorodetskii V. V. On the strong mixing property for linear sequences. Theory Probab. Appl. 22:1977;411-413.
15. Hall P., Heyde C. C. Martingale Limit Theory and Its Applications. 1980;Academic Press, New York.
16. Ibragimov I. A., Linnik Yu. V. Independent and Stationary Sequences of Random Variables. 1971;Walters-Noordhoff, Amsterdam.
17. Kang S., Koehler K. J. Modification of the Greenwood formula for correlated response times. Biometrics. 53:1997;885-899.
18. Kaplan E. L., Meier P. Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53:1958;457-481.
19. Koehler K. J. An analysis of temperature effects on bean leaf egg hatch times. Proceedings of the 1994 KSU Conference on Applied Statistics in Agriculture. 1995;Kansas State Univ. Press. p. 215-229.
20. Koehler K. J., Symanowski J. Constructing multivariate distributions with specific marginal distributions. J. Multivariate Anal. 55:1995;261-282.
21. N. N. Leonenko, and, L. M. Sakhno, On the Kaplan-Meier estimator of long-range dependent sequences, unpublished manuscript, 2000.
22. Masry E., Tjøstheim D. Nonparametric estimation and identification of nonlinear ARCH time series: Strong convergence and asymptotic normality. Econ. Theory. 11:1995;258-289.
23. Masry E., Tjøstheim D. Additive nonlinear ARX time series and projection estimates. Econ. Theory. 13:1997;214-252.
24. Peterson A. V. Expressing the Kaplan-Meier estimator as a function of empirical subsurvival functions. J. Amer. Statist. Assoc. 72:1977;854-858.
25. Shao Q.-M., Yu H. Weak convergence for weighted empirical processes of dependent sequences. Ann. Probab. 24:1996;2098-2127.
26. Shorack G. R., Wellner J. A. Empirical Processes with Applications to Statistics. 1986;Wiley, New York.
27. Shumway R. H., Azari A. S., Johnson P. Estimating mean concentrations under transformation for environmental data with detection limits. Technometrics. 31:1988;347-356.
28. Stute W., Wang J. L. A strong law under random censorship. Ann. Statist. 21:1993;1591-1607.
29. Tucker H. A Graduate Course in Probability. 1967;Academic Press, New York.
30. Voelkel J., Crowley J. Nonparametric inference for a class of semi-Markov process with censored observation. Ann. Statist. 12:1984;142-160.
31. Wang J. G. A note on the uniform consistency of the Kaplan-Meier estimator. Ann. Statist. 15:1987;1313-1316.
32. Wei L. J., Lin D. Y., Weissfeld L. Regression analysis of multivariate incomplete failure times data by modeling marginal distributions. J. Amer. Statist. Assoc. 84:1989;1064-1072.
33. Withers C. S. Conditions for linear processes to be strong mixing. Z. Wahrsch. verw. Gebiete. 57:1981;477-480.
34. Ying Z., Wei L. J. The Kaplan-Meier estimate for dependent failure time observations. J. Multivariate Anal. 50:1994;17-29.
35. Yu H. A Glivenko-Cantelli Lemma and weak convergence for empirical processes of associated sequences. Probab. Theory Related Fields. 95:1993;357-370.