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. This article has supplementary material online.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 808-825 |
| Number of pages | 18 |
| Journal | JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS |
| Volume | 19 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 2010 |
| Externally published | Yes |
Bibliographical note
Funding Information:Genton’s research was supported in part by NSF grants CMG ATM-0620624 and DMS-1007504, and by award no. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors are grateful to Thibault Laurent for implementing the hair-plot function in R and thank the editor, an associate editor, and two anonymous referees for their valuable comments.
Keywords
- Autocovariance
- Moran's I
- Outlier
- Quadratic form
- Robustness
- Space
- Time
- Variogram
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Statistics and Probability
- Statistics, Probability and Uncertainty