Visualizing Influential Observations in Dependent Data
We introduce the hair-plot to visualize influential observations in dependent data. It consists of all trajectories of the value of an estimator when each observation is modified in turn by an additive perturbation. We define two measures of influence: the local influence which describes the rate of departure from the original estimate due to a small perturbation of each observation; and the asymptotic influence which indicates the influence on the original estimate of the most extreme contamination for each observation. The cases of estimators defined as quadratic forms or ratios of quadratic forms are investigated in detail. Sample autocovariances, covariograms and variograms belong to the first case. Sample autocorrelations, correlograms, and indices of spatial autocorrelation such as Moran’s I belong to the second case. We illustrate our approach on various datasets from time series analysis and spatial statistics.
|Date of creation:||23 Jun 2009|
|Date of revision:|
|Publication status:||Published in Journal of Computational and Graphical Statistics, vol. 19, n°4, 2010, p. 808-825.|
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- Marc G. Genton & André Lucas, 2000.
"Comprehensive Definitions of Breakdown-Points for Independent and Dependent Observations,"
Tinbergen Institute Discussion Papers
00-040/2, Tinbergen Institute.
- Marc G. Genton & André Lucas, 2003. "Comprehensive definitions of breakdown points for independent and dependent observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 81-94.
- Hillier, Grant & Martellosio, Federico, 2006.
"Spatial design matrices and associated quadratic forms: structure and properties,"
Journal of Multivariate Analysis,
Elsevier, vol. 97(1), pages 1-18, January.
- Grant Hillier & Federico Martellosio, 2004. "Spatial design matrices and associated quadratic forms: structure and properties," CeMMAP working papers CWP16/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Hillier, Grant & Martellosio, Federico, 2006. "Spatial design matrices and associated quadratic forms: structure and properties," MPRA Paper 15807, University Library of Munich, Germany.
- Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew-"t" and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, 04.
- Gorsich, David J. & Genton, Marc G. & Strang, Gilbert, 2002. "Eigenstructures of Spatial Design Matrices," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 138-165, January.
- Genton, Marc G., 1999. "The correlation structure of the sample autocovariance function for a particular class of time series with elliptically contoured distribution," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 131-137, January.
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