Identifying Regression Outliers and Mixtures Graphically

By R. Dennis Cook, Frank Critchley. 2000

89 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/cb961b99cb32873d511d1afe9e93b1109dc5dd78

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In Statistics and Probability

Citations in the corpus

A note On outlier sensitivity of Sliced Inverse Regression (2002, background): “This might be a desired effect following Cook and Critchley (2000), who model the occurrence of possible outliers by assuming a mixture model.”
Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods (2003, background): “Cook and Critchley (2000) proved that once the data are “sliced,” the space spanned by SIR’s estimated matrix is a subspace of the space spanned by SAVE’s.”
Sufficient Dimension Reduction via Inverse Regression (2005, methodology): “Sufficient Dimension Reduction via Inverse Regression: A Minimum Discrepancy Approach”
On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, methodology): “…squares (OLS; Li and Duan 1989), principal Hessian directions (PHD; Li 1992), SIR, sliced average variance estimator (SAVE; Cook and Weisberg 1991; Cook and Critchley 2000), kernel inverse regression (Zhu and Fang 1996; Ferre and Yao 2005), structure adaptive estimator (Hristache, Juditsky,…”
Dimension reduction for the conditional kth moment in regression (2002, background): “Cook and Li (2001) introduced a new class of subspaces, which they called central mean subspaces, and studied their properties.”
Marginal tests with sliced average variance estimation (2007, methodology): “Sliced average variance estimation has been used by Cook & Critchley (2000) to identify outliers and mixtures graphically, by Bura & Pfeiffer (2003) for class prediction with DNA microarray data and by Zhu & Hastie (2003) in feature extraction for nonparametric discriminant analysis.”
On Directional Regression for Dimension Reduction (2007, background): “This result is from Ye and Weiss (2003); the sample version of this relation was shown earlier by Cook and Critchley (2000).”
Asymptotics for sliced average variance estimation (2007, background): “ASYMPTOTICS FOR SAVE 3 It is worth pointing out that the study of SAVE should receive more attention, as several papers have revealed that SAVE is more comprehensive than SIR: under regularity conditions, the CDR space of SAVE actually contains that of SIR (see [6, 24]).”
Optimal sufficient dimension reduction in regressions with categorical predictors (2002, background): “…of the outcomes of conditional dimension reduction becomes unwieldy when the qualitative predictor W has several levels, especially if dependencies between X and W increase the likelihood that the linear combinations relevant for each subpopulation regression differ [Cook and Critchley (2000)].”
Detection of single influential points in OLS regression model building (2001, methodology): “Cook and Critchley [46] used the theory of regression graphics based on central subspaces to construct a graphical solution to the long-standing problem of estimating the central subspace to identify outliers without specifying a model, and this method is also used in STAT [47].”
Testing predictor contributions in sufficient dimension reduction (2004, methodology): “994)investigated inference methodsfor d whenthe predictorsfollow an elliptically contoured distribution. Elliptically contoured distributions are not required for the general methods in this article. Cook and Critchley (2000) showed that SDR methods can be useful for identifying outliers and regress”
A general theory for nonlinear sufficient dimension reduction: Formulation and estimation (2013, background): “;(3) see Cook and Critchley (2000), Ye and Weiss (2003), Li, Zha and Chiaromonte (2005) and Li and Wang (2007).”