收缩邻域上样本中位数的MSE的高阶渐近性
Higher order asymptotics for the MSE of the sample median on shrinking neighborhoods
摘要：
我们提供了一个渐近展开的最大均方误差（MSE）的样本中位数要达到的收缩疏失误差附近的一个理想的中心分布。更具体地说，这种扩展是n^{-1/2}的幂，n是样本量，并且也使用n^{-1/2}的收缩率。这改进了Rieder[94]中一阶渐近性的相应结果。与通常的高阶渐近相反，我们首先不近似分布函数（或密度），而是直接扩展风险。我们的研究结果进行了说明，通过比较它们的模拟研究的结果和数值评估的精确MSE的理想和污染的情况下。
英文摘要：
We provide an asymptotic expansion of the maximal mean squared error (MSE) of the sample median to be attained on shrinking gross error neighborhoods about an ideal central distribution. More specifically, this expansion comes in powers of n^{-1/2}, for n the sample size, and uses a shrinking rate of n^{-1/2} as well. This refines corresponding results of first order asymptotics to be found in Rieder[94]. In contrast to usual higher order asymptotics, we do not approximate distribution functions (or densities) in the first place, but rather expand the risk directly. Our results are illustrated by comparing them to the results of a simulation study and to numerically evaluated exact MSE's in both ideal and contaminated situation.
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