Generalized MLE of a Joint Distribution Function with Multivariate Interval-Censored Data

We consider the problem of estimation of a joint distribution function of a multivariate random vector with interval-censored data. The generalized maximum likelihood estimator of the distribution function is studied and its consistency and asymptotic normality are established under the case 2 multivariate interval censorship model and discrete assumptions on the censoring random vectors.

[1]  J. Crowley,et al.  Correction: A Large Sample Study of Generalized Maximum Likelihood Estimators from Incomplete Data via Self-Consistency , 1985 .

[2]  M. Laan Efficient estimation in the bivariate censoring model and repairing NPMLE , 1996 .

[3]  R. Peto,et al.  Experimental Survival Curves for Interval‐Censored Data , 1973 .

[4]  J. Wellner,et al.  Information Bounds and Nonparametric Maximum Likelihood Estimation , 1992 .

[5]  Zhiliang Ying,et al.  A simple nonparametric estimator of the bivariate survival function under univariate censoring , 1993 .

[6]  Anton Schick,et al.  Asymptotic properties of the GMLE with case 2 interval-censored data , 1998 .

[7]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[8]  G. Y. Wong,et al.  Asymptotic properties of the GMLE in the case 1 interval‐censorship model with discrete inspection times , 1998 .

[9]  B. Turnbull The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data , 1976 .

[10]  Gregory Campbell,et al.  Nonparametric bivariate estimation with randomly censored data , 1981 .

[11]  J A Hanley,et al.  Nonparametric estimation of a multivariate distribution in the presence of censoring. , 1983, Biometrics.

[12]  D. Clayton,et al.  Multivariate generalizations of the proportional hazards model , 1985 .

[13]  D. Clayton A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[14]  Lin Li,et al.  Asymptotic Properties of Self-Consistent Estimators with Doubly-Censored Data , 2001 .

[15]  Richard D. Gill,et al.  Multivariate Survival Analysis , 1993 .

[16]  Dorota M. Dabrowska,et al.  Kaplan-Meier Estimate on the Plane , 1988 .

[17]  Jianwen Cai,et al.  Covariance and survivor function estimation using censored multivariate failure time data , 1992 .

[18]  J. Kongerud,et al.  Interval censoring in longitudinal data of respiratory symptoms in aluminium potroom workers: a comparison of methods. , 1994, Statistics in medicine.

[19]  Grace L. Yang,et al.  Strong Consistency of a Nonparametric Estimator of the Survival Function with Doubly Censored Data , 1987 .

[20]  Sue Leurgans,et al.  Nonparametric Estimation of a Bivariate Survival Function in the Presence of Censoring , 1986 .