论文标题
多元正常性的测试 - 重点是加权$ l^2 $统计学的批判性评论
Tests for multivariate normality -- a critical review with emphasis on weighted $L^2$-statistics
论文作者
论文摘要
本文对I.I.D.设定的多元正态性仿射不变测试的新发展进行了介绍，并特别强调了几类加权$ l^2 $统计量的几类的渐近性能。由于加权$ l^2 $统计量通常在固定替代方案下具有限制正常分布，因此它们为正态性的模型验证附近开放。本文还回顾了有关此问题的其他几项不变测试，尤其是能量测试，并提出了一项大规模仿真研究的结果。所有研究的测试均在随附的R-pakeAge MNT中实施。
This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of weighted $L^2$-statistics. Since weighted $L^2$-statistics typically have limit normal distributions under fixed alternatives to normality, they open ground for a neighborhood of model validation for normality. The paper also reviews several other invariant tests for this problem, notably the energy test, and it presents the results of a large-scale simulation study. All tests under study are implemented in the accompanying R-package mnt.
