Abstract

The local influence analysis is useful for identifying influential observations in statistical diagnostics and sensitivity analysis. However, it is often criticized for lack of a rigorous criterion to judge the influence magnitude from the elements of the main diagnostic. In this paper, a new method, call sparse local influence analysis, is proposed to detect the influential observations. We establish the connection between local influence analysis and sparse principal component analysis and propose a modified local diagnostic with sparse elements, i.e., diagnostic with very few nonzero elements. With this method, influential observations can be efficiently detected by the nonzero elements of the modified diagnostic. Two real data sets are used for illustration and simulation studies are conducted to confirm the efficiency of the proposed methodology.

摘要

局部影响分析对于在统计诊断和敏感性分析中识别有影响的观察是有用的。然而，由于缺乏严格的标准来判断主要诊断要素的影响程度，因此经常受到批评。在本文中，提出了一种称为稀疏局部影响分析的新方法来检测有影响的观测值。我们建立了局部影响分析和稀疏主成分分析之间的联系，并提出了一种改进的稀疏元素局部诊断，即非零元素很少的诊断。使用这种方法，可以通过修改后的诊断的非零元素有效地检测有影响的观察结果。