关于渐近中位无偏估计的渐近效率(英文)

On Asymptotic Efficiency Under Asymptotically Median Unbiased Estimate *

本文在几种重要的分布族中，给出了渐近中位无偏估计的渐近效率的一种定义。给出了如下一些结果：在单参数族中，提出了构造渐近有效的渐近中位无偏估计的一种方法，在具有共同支撑集的分布族中，论证了渐近中位无偏有效估计与ＢＡＮ估计之间的等价值；而在非共同支撑集的截断族中，对一般的参数向量函数构造了它们的渐近中位无偏估计，并且计算出了它们的渐近效率。

The asymptotic efficiency of estimates,under the restriction of asymptotically median unbiased estimates,of a general function of parameter vector is addressed in several kinds of distribution families.In the single parameter family,a method to find asymptotically efficient estimate is given.In the family with common support,equivalent relations between asymptotically efficient estimate and best asymptotic normal estimate is proved,and in the family without common support,the asymptotically median unbiased estimates of general parameter vector function have been constructed,and the asymptotic efficiencies have been calculated.