Uniformly Minimum Variance Estimation in Location Parameter Families
位置参数族中的一致最小方差估计
Let $x_1, \cdots, x_n$ be a sample of size $n$ of an $\operatorname{rv}$ with $\operatorname{df} F(x - \theta)$, where $F$ is known but $\theta$ unknown. In this paper we make a Fourier approach to the problem of existence of a statistic $g(x_1, \cdots, x_n)$ which is a uniformly minimum variance (UMV) estimator of its own mean value. We mention only some of the results. If $n = 1$ we find an NASC for an estimator $g(x_1)$ to be, in a restricted sense, UMV. This condition is…