Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 2, pp. 176-183

ASYMPTOTIC VARIANCE OF THE GMLE OF A SURVIVAL FUNCTION WITH INTERVAL-CENSORED DATA

By

QIQING YU, State University of New York at Binghamton, New York
LINXIONG LI,University of New Orleans, Los Angeles
GEORGE Y.C. WONG, Strang Cancer Preventive Center, New York

SUMMARY. Interval-censored data are generated by a random survival time $X$ and a random censoring interval. We either observe the exact survival time or only know the survival time lies within the censoring interval. Turnbull (1976) proposes a self-consistent algorithm for obtaining the generalized maximum likelihood estimator (GMLE) of a survival function with interval-censored data. Yu, Li and Wong (1996) prove the strong consistency of the GMLE. In this paper, we establish the asymptotic normality of the GMLE and self-consistent estimators (SCE) and present a consistent estimator of the asymptotic variance of the GMLE and SCEs with interval-censored data.

AMS (1991) subject classification.Primary 62G05; secondary 62G20.

Key words and phrases. Asymptotic normality, generalized MLE, self-consistent estimate, survival analysis.

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