Asymptotic normality of the truncation probability estimator for truncated dependent data

Document Type : Research Article

Authors

S. Jomhoori

V. Fakoor

H. A. Azarnoosh

10.22067/ijnao.v2i1.639

Abstract

In some long term studies, a series of dependent and possibly truncated life-times may be observed. Suppose that the lifetimes have a common marginal distribution function. In left-truncation model, one observes data (Xi,Ti)
only, when Ti ≤ Xi. Under some regularity conditions, we provide a strong representation of the ßn estimator of ß = P(Ti ≤ Xi), in the form of an average of random variables plus a remainder term. This representation en-ables us to obtain the asymptotic normality for ßn .

Keywords

a-mixing

left-truncation

product-limit estima- tor

strong representation

truncation probability

20.1001.1.24236977.2009.2.1.5.7

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