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Geometric aspects of deletion diagnostics in multivariate regression

机译：多元回归中删除诊断的几何方面

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摘要

In multivariate regression, a graphical diagnostic method of detecting observations that are influential in estimating regression coefficients is introduced. It is based on the principal components and their variances obtained from the covariance matrix of the probability distribution for the change in the estimator of the matrix of unknown regression coefficients due to a single-case deletion. As a result, each deletion statistic obtained in a form of matrix is transformed into a two-dimensional quantity. Its univariate version is also introduced in a little different way. No distributional form is assumed. For illustration, we provide a numerical example in which the graphical method introduced here is seen to be effective in getting information about influential observations.
机译：在多元回归中，引入了一种图形诊断方法，用于检测对估计回归系数有影响的观察结果。它基于从概率分布的协方差矩阵中获得的主成分及其方差，该因数是由于单例删除而导致的未知回归系数矩阵的估计量变化的概率分布。结果，以矩阵形式获得的每个删除统计量被转换为二维量。它的单变量版本也以稍微不同的方式引入。不假定分配形式。为了说明，我们提供了一个数值示例，其中，此处介绍的图形方法被视为可有效获取有关影响观测的信息。

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