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.
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