广义区间估计及其最优性(Ⅰ)

Generalized Interval Estimation and Its Most Goodness (Ⅰ)

将普通区间估计的概念(x1,x2,…,xn)→[G1(x1,x2,…,xn),G2(x1,x2,…,xn)]拓广为广义区间估计的概念(x1,x2,…,xn)→{Aλ｜Aλ∈ Θ,Aλ∩[G1(x1,x2,…,xn),G2(x1,x2,…,xn)]≠ }.于广义区间估计上建立了最优性概念,证明了广义区间估计与假设检验的最优性之间的关系,推演了一个重要区间估计的最优性.

In this paper, the ordinal interval estimation(x1,x2,…,xn)→[G1(x1,x2,…,xn),G2(x1,x2,…,xn)]is expanded to its generalized form(x1,x2,…,xn)→{Aλ|Aλ∈,Aλ∩[G1(x1,x2,…,xn),G2(x1,x2,…,xn)]≠}.The concept of most goodness for the generalized interval estimation is established. The relationship between generalized interval estimation and hypothesis testing is discussed. The most goodness of a sort of generalized interval estimation is deduced.