Perturbation selection and influence measures in local influence analysis. (English) Zbl 1129.62068
Summary: R. D. Cook’s [J. R. Stat. Soc., Ser. B 48, 133–169 (1986; Zbl 0608.62041)] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous approach has been developed to address two fundamental issues: the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative. The aim of this paper is to develop a differential-geometrical framework of a perturbation model (called the perturbation manifold) and utilize the associated metric tensor and affine curvatures to resolve these issues.
We show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model. Moreover, we introduce new influence measures that are applicable to objective functions at any point. Examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations.
We show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model. Moreover, we introduce new influence measures that are applicable to objective functions at any point. Examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations.
MSC:
| 62J20 | Diagnostics, and linear inference and regression |
| 53C99 | Global differential geometry |
| 53B99 | Local differential geometry |
Citations:
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