The asyrmptotic properties of the self-consistent estimator (SCE) of a distribution function F of a random variable X with doubly-censored data are examined by several authors under the asstumption that X is observabl...The asyrmptotic properties of the self-consistent estimator (SCE) of a distribution function F of a random variable X with doubly-censored data are examined by several authors under the asstumption that X is observable everywhere in the interval [a, b], where a=inf{x: F(x)】0} and b=sup{x: F(x)【1}. Such an assumption does not allow the situation that X is discrete and the situation that X is only observable in a nontrivial subinterval of [a, b]. However, often in practice this assumption is not satisfied. In this manuscript we establish strong uniform consistency, asymptotic normality and asymptotic efficiency of the SCE under a set of assumptions that allow the situation that X is discrete and the situation that X is only observable in a nontrivial subinterval of [a, b]. Finally, we point out a gap in the proofs of the existing results in the literature due to the definition of the SCE.展开更多
基金Supported by Grants DMS-9402561, DAMD17-94-J-4332 DAMD17-99-1-9390Supported by BoRSF Grant RD-A-31.
文摘The asyrmptotic properties of the self-consistent estimator (SCE) of a distribution function F of a random variable X with doubly-censored data are examined by several authors under the asstumption that X is observable everywhere in the interval [a, b], where a=inf{x: F(x)】0} and b=sup{x: F(x)【1}. Such an assumption does not allow the situation that X is discrete and the situation that X is only observable in a nontrivial subinterval of [a, b]. However, often in practice this assumption is not satisfied. In this manuscript we establish strong uniform consistency, asymptotic normality and asymptotic efficiency of the SCE under a set of assumptions that allow the situation that X is discrete and the situation that X is only observable in a nontrivial subinterval of [a, b]. Finally, we point out a gap in the proofs of the existing results in the literature due to the definition of the SCE.
