摘要
For the two side truncated distribution family: dPθ(x) = f(x;θ1θ2)I(θ≤ x≤θ2)dx, where θ=(θ1,θ2),θ < θ2,chen & Fu studied one side asymptotic efficiency of the estimator for parameter hation g(θ) = c1θ1 + C2θ2, they pointed out that when c1c2≥0, there exist one side asymptotic efficient estimators for g(θ); when c1c2 < 0, the estimator they proposed is not asymptotically efficient. Then they put forward a question: Is there any other asymptotically efficient estimator for g(θ) when c1c2 <0? In this paper, we study this problem, we prove that when the distribution under consideration is uniform distribution with location and scale parameters, there does not exist one side asymptotically efficient estimators for the scale parameter.
For the two side truncated distribution family: dPθ(x) = f(x;θ1θ2)I(θ≤ x≤θ2)dx, where θ=(θ1,θ2),θ < θ2,chen & Fu studied one side asymptotic efficiency of the estimator for parameter hation g(θ) = c1θ1 + C2θ2, they pointed out that when c1c2≥0, there exist one side asymptotic efficient estimators for g(θ); when c1c2 < 0, the estimator they proposed is not asymptotically efficient. Then they put forward a question: Is there any other asymptotically efficient estimator for g(θ) when c1c2 <0? In this paper, we study this problem, we prove that when the distribution under consideration is uniform distribution with location and scale parameters, there does not exist one side asymptotically efficient estimators for the scale parameter.
