Asymptotic normality of the truncation probability estimator for truncated dependent data

Iranian Journal of Numerical Analysis and Optimization

مقاله 4، دوره 2، شماره 1 - شماره پیاپی 2، فروردین 2009   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v2i1.639

نویسندگان

S. Jomhoori؛ V. Fakoor^* ؛ H. A. Azarnoosh

چکیده

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 .

کلیدواژه‌ها

a-mixing؛ left-truncation؛ product-limit estima- tor؛ strong representation؛ truncation probability