TY - JOUR
T1 - Survival analysis for the missing censoring indicator model using kernel density estimation techniques
AU - Subramanian, Sundarraman
N1 - Funding Information:
I am grateful to referees and an Associate Editor for their useful comments, and to Prof. Jogesh Babu for allowing a revision. Thanks are also due to Prof. Peter Major for explaining a technicality in his published paper with Prof. L. Rejtő. This research was initiated during the author’s sabbatical leave at the University of Maine in Fall 2003. Research partly supported by National Institutes of Health grant CA 103845.
PY - 2006/4
Y1 - 2006/4
N2 - This article concerns asymptotic theory for a new estimator of a survival function in the missing censoring indicator model of random censorship. Specifically, the large sample results for an inverse probability-of-non- missingness weighted estimator of the cumulative hazard function, so far not available, are derived, including an almost sure representation with rate for a remainder term, and uniform strong consistency with rate of convergence. The estimator is based on a kernel estimate for the conditional probability of non-missingness of the censoring indicator. Expressions for its bias and variance, in turn leading to an expression for the mean squared error as a function of the bandwidth, are also obtained. The corresponding estimator of the survival function, whose weak convergence is derived, is asymptotically efficient. A numerical study, comparing the performances of the proposed and two other currently existing efficient estimators, is presented.
AB - This article concerns asymptotic theory for a new estimator of a survival function in the missing censoring indicator model of random censorship. Specifically, the large sample results for an inverse probability-of-non- missingness weighted estimator of the cumulative hazard function, so far not available, are derived, including an almost sure representation with rate for a remainder term, and uniform strong consistency with rate of convergence. The estimator is based on a kernel estimate for the conditional probability of non-missingness of the censoring indicator. Expressions for its bias and variance, in turn leading to an expression for the mean squared error as a function of the bandwidth, are also obtained. The corresponding estimator of the survival function, whose weak convergence is derived, is asymptotically efficient. A numerical study, comparing the performances of the proposed and two other currently existing efficient estimators, is presented.
KW - Bandwidth sequence
KW - Functional delta method
KW - Independent increments
KW - Kernel density estimator
KW - Lyapounov central limit theorem
KW - Standard Wiener process
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U2 - 10.1016/j.stamet.2005.09.014
DO - 10.1016/j.stamet.2005.09.014
M3 - Article
AN - SCOPUS:33644501816
SN - 1572-3127
VL - 3
SP - 125
EP - 136
JO - Statistical Methodology
JF - Statistical Methodology
IS - 2
ER -