双向删失数据情形下的置信限

CONFIDENCE LIMITS IN THE CASE OF DOUBLE CENSORING

设X_1,X_2,…,X_n是概率空间(Ω,f,P_e)(θ∈①)上的独立同分布随机变量列,共同分布函数是F(x,θ).(F(0,θ)=0).给定正数t_1,…,t_n及函数9(θ):①→[-∞,∞].设Y_i=l(X_i>t_i)(i=1,2,…,n),这里l_A是集合A的示性函数。本文中我们给出了9(θ)的基于观测值y=(y_1,y_2,…,y_n)的最优的置信下限,当①=((?),(?)) (-∞≤(?)<(?)≤∞)而且F(t_i,θ)是θ的严格减函数时,我们得到了计算最优置信限的有效方法。

Let X_1, X_2, …, X_n be a sequence of random variables which are independently and identically distributed on probability space (Ω, F, P_θ) (0∈0) with distribution function F(x, θ). Given t_1, t_2, …, t_n (positive numbers) and g(θ): Θ→[-∞, ∞]. Let Y_i=I(X_i>t_i) (i=1, …, n), where I(A) is an indicator of the set A. In the present paper, we give the best lower confidence limits for g(θ) based on observed Y=(Y_1, Y_2, …, Y_n). When Θ=((?), (?)) (-∞≤(?)<(?)≤∞) and F(t_i, θ) is strictly deoreasing ror θ, we obtain an efficient method for constructing the best confidence limit.