双边截断分布族中的卷积定理与渐近有效性

Convolution Theorem and Asymptotic Efficiency in Two Side Truncated Distribution Families

在具有共同支撑的分布族与单边截断分布族中，Ｂｉｃｋｌｅ Ｐ．Ｊ， Ｉｂｒａｇｉｍｏｖ Ｉ． Ａ． 与 Ｈａｓｍｉｎｓｋｉｉ Ｒ． Ｚ．证明了两个重要的卷积定理．在本文中，我们考虑如下的双边截断分布族：ｄＰθ（ｘ）＝ ｆ（ｘ； θ１， θ２）Ｉ（θ１≤ｘ≤ θ２）ｄｘ，其中θ＝（θ１， θ２）， θ１＜ θ２为未知 待估参数．在较弱的条件下，我们得到了关于此分布族的卷积定理．并且，基于此卷 积定理的结论，提出了一个参数函数渐近有效性的定义．在本文结束之时，对于一个 双边截断分布族，给出了具有此渐近有效性的参数函数的估计．

In the common support distribution and one side truncated distribution families, Bickle, Ibragimov I. A. and Hasminskii R. Z. proved two important convolution theorems. In this paper, we consider the following two side truncated distribution families: dPθ(x) = j(x;θ1,θ2)I(θ1 ≤x≤θ2)dx, where θ= (θ1,θ2), θ1 <θ2 are unknown. Under some weak conditions, we get convolution theorem, furthermore, based on the result, a new asymptotic efficiency definition is proposed. At the end of the paper, we construct some asymptotic efficient estimators for one class of two side truncated distribution families.