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Visualizing Influential Observations in Dependent Data

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  • Genton, Mark G.
  • Ruiz-Gazen, Anne

Abstract

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.

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Bibliographic Info

Paper provided by Toulouse School of Economics (TSE) in its series TSE Working Papers with number 09-051.

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Date of creation: 23 Jun 2009
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Publication status: Published in Journal of Computational and Graphical Statistics, vol.�19, n°4, 2010, p.�808-825.
Handle: RePEc:tse:wpaper:22176

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Keywords: autocovariance; Moran's I; outlier;

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References

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  1. 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.
  2. Hillier, Grant & Martellosio, Federico, 2006. "Spatial design matrices and associated quadratic forms: structure and properties," MPRA Paper 15807, University Library of Munich, Germany.
  3. 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.
  4. 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.
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Cited by:
  1. Li, Hongfei & Calder, Catherine A. & Cressie, Noel, 2012. "One-step estimation of spatial dependence parameters: Properties and extensions of the APLE statistic," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 68-84.

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