论文标题
通过平衡不完整的U统计数据近似散射的对称估计量
Approximating Symmetrized Estimators of Scatter via Balanced Incomplete U-Statistics
论文作者
论文摘要
我们得出了散布对称估计量的限制分布，而不是所有$ n（n-1）/2 $ $ n $观测值，我们仅考虑$ nd $ $ nd $适当选择的对，$ 1 \ le d <\ lfloor n/2 \ rfloor $。事实证明，每当$ d = d（n）\ to \ infty $以任意缓慢的速度时，所得估计器渐近地等同于原始估计器。我们还调查了任意固定$ D $的渐近属性。这些考虑因素和数值示例表明，出于实际目的，中等固定的固定值$ d $之间，例如$ 10 $和20 $的收益率已经在计算上是可行的，并且与原始的估计值很近。
We derive limiting distributions of symmetrized estimators of scatter, where instead of all $n(n-1)/2$ pairs of the $n$ observations we only consider $nd$ suitably chosen pairs, $1 \le d < \lfloor n/2\rfloor$. It turns out that the resulting estimators are asymptotically equivalent to the original one whenever $d = d(n) \to \infty$ at arbitrarily slow speed. We also investigate the asymptotic properties for arbitrary fixed $d$. These considerations and numerical examples indicate that for practical purposes, moderate fixed values of $d$ between,say, $10$ and $20$ yield already estimators which are computationally feasible and rather close to the original ones.
