| Summary: | 碩士 === 東海大學 === 統計學系 === 97 === Let (T1; T2) denote the lifetimes of two competing risks of interest and can be dependent
on each other. Let V and (T3;C) denote left truncation and right censoring variables, respectively,
where C denotes the censoring time due to termination of the follow-up period, and
T3 is the censoring time due to a failure other than the two failures of interest, which might
occur before the cross-section time. Assume that (T1; T2), (V;C) and T3 are independent of
one another other but V and C are dependent with P(C _ V ) = 1. Let aG denote the left
support of V . In application, due to truncation, some a > aG is selected so that the size of
the observed risk set at a is not too small. Let _1(xja) = P(T1 _ x; T1 _ T2jT1 > a; T2 > a)
and _2(xja) = P(T2 _ x; T2 _ T1jT1 > a; T2 > a) denote the conditional cumulative incidence
function of T1 and T2, respectively. When V is uniformly distributed and C = T3 = 1,
Huang and Wang (1995) proposed a semiparametric estimator of _k(xj0). In this article, we
extend previous models by considering the case when the distribution of V is parameterized
as G(x; _) and the distributions of Tk and C are left unspeci_ed. Several iterative algorithms
are proposed to obtain the semiparametric estimates (denoted by _k(x; ^_nja)) of _k(xja).
The consistency of _k(x; ^_nja) is derived. Simulation results show that the semiparametric
estimators _k(x; ^_nja) have smaller mean squared errors compared to the nonparametric
maximum likelihood estimator of _k(xja).
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