Leverage, residual, and interaction diagnostics for subsets of cases in least squares regression

Barrett, Bruce E.; Gray, J. Brian

doi:10.1016/s0167-9473(97)00022-4

Cited by 18 publications

(7 citation statements)

References 22 publications

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“…J ||, the Frobenius matrix norms of the sub-matrices of H, since they are not measure-specific and easy to compute (see Barrett and Gray, 1997). The measure ||H I || quantifies the leverage for observations outside subset J corresponding to a RQ, i.e., observations i ∈ I .…”

Section: Proof Of (Iii)mentioning

confidence: 99%

“…For instance, there may be situations where observations are individually influential (in the high leverage sense), but not jointly. Furthermore, joint influence is difficult to understand and detect since the computational demands may be huge (see, e.g., Barrett and Gray, 1997) and therefore practically infeasible.…”

Section: Introductionmentioning

confidence: 99%

“…b Subset diagnostics are not comparable across different subset sizes (see e.g., Barrett and Gray, 1997). So a different subset size m = p is not useful for comparison purposes, hence we fix the subset size at m = p.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multiple Case High Leverage Diagnosis in Regression Quantiles

Ranganai

Vuuren

Wet

2014

Communications in Statistics - Theory and Methods

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Section: Proof Of (Iii)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiple Case High Leverage Diagnosis in Regression Quantiles

Ranganai

Vuuren

Wet

2014

Communications in Statistics - Theory and Methods

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“…For instance, a first group of works reformulated the Cook distance to handle subsets of cases [4]. Other approaches try to introduce a robust component in these measures.…”

Section: Introductionmentioning

confidence: 99%

Discriminative Hat Matrix: A new tool for outlier identification and linear regression

Dufrenois¹,

Noyer²

2011

The 2011 International Joint Conference on Neural Networks

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The hat matrix is an important auxiliary quantity in linear regression theory for detecting errors in predictors. Traditionally, the comparison of the diagonal elements with a calibration point serves as decision rule for separating a dominant linear population from outliers. However, several problems exist : first, the calibration point is not well defined because no exact statistical distribution (asymptotic form) of the hat matrix diagonal exists [1]. Secondly, being based on the standard covariance matrix, this outlying measure looses its efficiency when the rate of "atypical" observations becomes large [2] [3]. In this paper, we present a discriminative version of the hat matrix (DHM) which transposes this classification problem into a subspace clustering problem. We propose a linear discriminant analysis based criterion directly built on the properties of the hat matrix and we show that its maximization leads to search an optimal projection subspace and an optimal indicator matrix. We also show that the statistic of the hat matrix diagonal "projected" on this optimal subspace has an exact χ 2 behaviour and thus makes it possible to identify outliers by way of hyptothesis testing. Synthetic data sets are used to study the performance both in terms of regression and classification of the proposed approach. We also illustrate its potential application to motion segmentation in image sequences.

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“…In regression the single-deletion diagnostics described in Cook and Weisberg (1982) and Atkinson (1985) may fail owing to 'maslung' if there is more than one outlier. More recent regression methods using multiple-deletion diagnostics, such as those of Barrett and Gray (1997) and Haslett (1999), may likewise fail either owing to masking or computational requirements and interpretability if there are too many outliers. For generalized linear models single-deletion methods are summarized in chapter 12 of McCullagh and Nelder (1989).…”

Section: Introductionmentioning

confidence: 99%

Regression Diagnostics for Binomial Data from the Forward Search

Atkinson

Riani

2001

J Royal Statistical Soc D

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Summary. We suggest a simple robust method for the detection of atypical and influential observations in binomial data. Our technique is based on a forward search procedure which orders the observations from those most in agreement with a specified generalized linear model to those least in agreement with it. The effectiveness of the forward search estimator in detecting masked multiple outliers, and more generally in ordering binomial data, is shown by means of three data sets. Plots of diagnostic quantities during the forward search clearly show the effect of individual observations on residuals and test statistics. These examples reveal the strength of our method in showing the structure of the data in a way which is more simple and effective than it would be by using standard deletion diagnostic procedures.

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Leverage, residual, and interaction diagnostics for subsets of cases in least squares regression

Cited by 18 publications

References 22 publications

Multiple Case High Leverage Diagnosis in Regression Quantiles

Multiple Case High Leverage Diagnosis in Regression Quantiles

Discriminative Hat Matrix: A new tool for outlier identification and linear regression

Regression Diagnostics for Binomial Data from the Forward Search

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