Controlling the size of multivariate outlier tests with the MCD estimator of scatter

Cerioli, Andrea; Riani, Marco; Atkinson, Anthony C.

doi:10.1007/s11222-008-9096-5

Cited by 31 publications

(20 citation statements)

References 22 publications

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“…Therefore, we follow the approach of Cerioli et al . (), and we resort to a different Monte Carlo approximation of

ς_{γ}^{2}

based on pooling all the n * = n × K estimates

ŝ_{[i]}^{2} (k)

in a single sample

Ŝ = {(ŝ_{[1]}^{2} (1), \dots, ŝ_{[1]}^{2} (K), ŝ_{[2]}^{2} (1), \dots, ŝ_{[2]}^{2} (K), \dots, ŝ_{[n]}^{2} (1), \dots, ŝ_{[n]}^{2} (K))}^{'} .

Motivated by convergence results (here as n * → ∞ ) for quantiles, even in the case of non‐independent observations (see, e.g. Korosok, ), we take the γ ‐th quantile of the pooled sample

Ŝ

as our estimate of

ς_{γ}^{2}

, that is,

{\overset{ς}{true}}_{γ}^{2} = Ŝ_{[l]},

where

Ŝ_{[l]}

is the l ‐th ordered value in

Ŝ

and l is defined as in , with n replaced by n * .…”

Section: Reliable Robust Diagnosticsmentioning

confidence: 99%

“…This tendency was first noted by Cook & Hawkins (), although in a somewhat biased context, and then confirmed in subsequent studies, even when ad hoc finite‐sample corrections are taken into account; see, for example, Cerioli et al . (), Fauconnier & Haesbroeck (), Cerioli et al . (), Lourenco & Pires () and Riani et al .…”

Section: Introductionmentioning

confidence: 95%

“…Cerioli et al . (), Riani et al . () and Cerioli () propose alternative strategies for overcoming this shortcoming in the multivariate framework, while Maronna & Yohai () develop specific corrections for regression MM‐estimates when the ratio p / n is large.…”

Section: Introductionmentioning

confidence: 95%

See 2 more Smart Citations

Reliable Robust Regression Diagnostics

Salini

Cerioli

Laurini

et al. 2015

Int Statistical Rev

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Motivated by the requirement of controlling the number of false discoveries that arises in several application fields, we study the behaviour of diagnostic procedures obtained from popular highbreakdown regression estimators when no outlier is present in the data. We find that the empirical error rates for many of the available techniques are surprisingly far from the prescribed nominal level. Therefore, we propose a simulation-based approach to correct the liberal diagnostics and reach reliable inferences. We provide evidence that our approach performs well in a wide range of settings of practical interest and for a variety of robust regression techniques, thus showing general appeal. We also evaluate the loss of power that can be expected from our corrections under different contamination schemes and show that this loss is often not dramatic. Finally, we detail some possible extensions that may further enhance the applicability of the method.

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“…Therefore, we follow the approach of Cerioli et al . (), and we resort to a different Monte Carlo approximation of

ς_{γ}^{2}

based on pooling all the n * = n × K estimates

ŝ_{[i]}^{2} (k)

in a single sample

Ŝ = {(ŝ_{[1]}^{2} (1), \dots, ŝ_{[1]}^{2} (K), ŝ_{[2]}^{2} (1), \dots, ŝ_{[2]}^{2} (K), \dots, ŝ_{[n]}^{2} (1), \dots, ŝ_{[n]}^{2} (K))}^{'} .

Motivated by convergence results (here as n * → ∞ ) for quantiles, even in the case of non‐independent observations (see, e.g. Korosok, ), we take the γ ‐th quantile of the pooled sample

Ŝ

as our estimate of

ς_{γ}^{2}

, that is,

{\overset{ς}{true}}_{γ}^{2} = Ŝ_{[l]},

where

Ŝ_{[l]}

is the l ‐th ordered value in

Ŝ

and l is defined as in , with n replaced by n * .…”

Section: Reliable Robust Diagnosticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

Reliable Robust Regression Diagnostics

Salini

Cerioli

Laurini

et al. 2015

Int Statistical Rev

Self Cite

View full text Add to dashboard Cite

show abstract

“…In fact, this was the view behind the seminal work of Wilks (1963). More recent appreciation of this requirement can be found in the techniques developed by Hadi (1994), Becker and Gather (1999), García-Escudero and Gordaliza (2005), Hardin and Rocke (2005) and Cerioli, Riani, and Atkinson (2009).…”

Section: One Multivariate Samplementioning

confidence: 99%

The forward search: Theory and data analysis

Atkinson

Riani

Cerioli

2010

Journal of the Korean Statistical Society

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a b s t r a c tThe Forward Search is a powerful general method, incorporating flexible data-driven trimming, for the detection of outliers and unsuspected structure in data and so for building robust models. Starting from small subsets of data, observations that are close to the fitted model are added to the observations used in parameter estimation. As this subset grows we monitor parameter estimates, test statistics and measures of fit such as residuals. The paper surveys theoretical development in work on the Forward Search over the last decade. The main illustration is a regression example with 330 observations and 9 potential explanatory variables. Mention is also made of procedures for multivariate data, including clustering, time series analysis and fraud detection.

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“…We also provided some corrections in the case of multivariate data, where Mahalanobis distances replace scaled residuals. Our improved methods involve both distributional results for finite samples and powerful ways of dealing with multiple outliers tests (Cerioli et al , ; Cerioli, ; Cerioli and Farcomeni, ). However, we acknowledge that a unified asymptotic theory of multivariate outlier detection has yet to come.…”

mentioning

confidence: 99%