On affine equivariant multivariate quantiles
On affine equivariant multivariate quantiles
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DOI：
10.1023/a:1012478908041
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发表时间：
2001-06-01
影响因子：
1
通讯作者：
Chakraborty, B
中科院分区：
文献类型：
--
作者：
Chakraborty, B
本文提出并研究了一元分位数在多元系统中的推广。所提出的方法是仿射等变的，它是基于自适应变换再变换过程。Bahadur型线性表示的建议分位数的建立，从而也得到了渐近分布。作为这些多元分位数的应用，我们开发了一些仿射等变分位数等高线图，可以用来研究数据云的几何形状以及潜在的概率分布和检测离群值。这些分位数也可以用来构造多变量Q-Q图的仿射不变版本，这在检查给定的多变量概率分布与数据的拟合程度以及比较两个数据集的分布方面很有用。我们说明了这些应用程序与一些模拟和真实的数据集。我们还指出了一种方法，扩展的概念，单变量L-估计和修剪的手段，在多变量设置使用这些仿射等变分位数。
An extension of univariate quantiles in the multivariate set-up has been proposed and studied. The proposed approach is affine equivariant, and it is based on an adaptive transformation retransformation procedure. Bahadur type linear representations of the proposed quantiles are established and consequently asymptotic distributions are also derived. As applications of these multivariate quantiles, we develop some affine equivariant quantile contour plots which can be used to study the geometry of the data cloud as well as the underlying probability distribution and to detect outliers. These quantiles can also be used to construct affine invariant versions of multivariate Q-Q plots which are useful in checking how well a given multivariate probability distribution fits the data and for comparing the distributions of two data sets. We illustrate these applications with some simulated and real data sets. We also indicate a way of extending the notion of univariate L-estimates and trimmed means in the multivariate set-up using these affine equivariant quantiles.