Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 1, pp. 67--79

ESTIMATION IN THE KOZIOL-GREEN MODEL WITH LEFT TRUNCATED OBSERVATIONS

By

JÖRG PAWLITSCHKO, Universitäat Dortmund, Dortmund

SUMMARY. The Koziol-Green (KG) model is a model of informative censoring where the survival function of the censoring times is assumed to be a power of the survival function $\ol{F}$ of the lifetimes. Taking advantage of this relationship leads to a better estimator of $\ol{F}$ than the commonly used Kaplan-Meier product-limit estimator. In this paper, a generalization of the KG model is introduced, where observations are allowed to be truncated from the left. Under this model, a semiparametric estimator of $\ol{F}$ is proposed and its asymptotic properties are investigated. In particular, it is shown that the new estimator is asymptotically more efficient than the standard product-limit estimator for left truncated and right censored data. To give an example of the applicability of this model and of this estimator, the well-known Channing House data are examined.

AMS (1991) subject classification. Primary 62N05; secondary 62G05, 62G20.

Key words and phrases. Random censoring; product-limit estimator; Kaplan-Meier estimator; ACL estimator; LIL; weak convergence.

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