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指定年龄下“新优于旧”约束生存函数估计量的弱收敛AI 解读

A survival function S is said to be in the New Better than Used of age t 0 (NBU-t 0) class if S(x + t 0) ≤ S(t 0)S(x) for all x ≥ 0. Reneau and Samaniego proposed an estimator Ŝ n for S when S is known as a member of the NBU-t 0 class. Many properties of Ŝ n were studied by Reneau and Samaniego. The problems of the weak convergence of Wn = √n (Ŝ n − S), however, was not solved. In this article, we show that the weak convergence of Wn does not hold in general and establish…

指定年龄下新优于旧约束的生存函数估计量弱收敛AI 解读

A survival function S is said to be in the New Better than Used of age t 0 (NBU-t 0) class if S(x + t 0) ≤ S(t 0)S(x) for all x ≥ 0. Reneau and Samaniego proposed an estimator Ŝ n for S when S is known as a member of the NBU-t 0 class. Many properties of Ŝ n were studied by Reneau and Samaniego. The problems of the weak convergence of Wn = √n (Ŝ n − S), however, was not solved. In this article, we show that the weak convergence of Wn does not hold in general and establish…

双重删失数据下生存函数自洽估计量的弱收敛AI 解读

Double censoring often occurs in collecting lifetime data and accordingly self-consistent estimators are widely employed for estimating the survival functions. In this paper we prove the weak convergence of self-consistent estimators using classical results on the Fredholm integral equation. Also, a method of calculating the asymptotic variance is presented.

双重删失数据下生存函数非参数估计量的强一致性AI 解读

A double censoring mechanism is such that each variable $X$ in the sample is observable if and only if $X$ is within the observation interval $\lbrack Z, Y \rbrack$. Otherwise, we can only determine whether $X$ is less than $Z$ or greater than $Y$ and observe $Z$ or $Y$ correspondingly. This kind of censoring occurs often in collecting lifetime data. Our problem is to estimate the survival function of $X, S_X(t) = P \lbrack X > t \rbrack$, from a doubly censored sample,…