Wei Xing SONG(1),Ping CHENG(2)
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.