New algorithms for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.gif" display="inline" overflow="scroll"><mml:mi>M</mml:mi></mml:math>-estimation of multivariate scatter and location

Dümbgen, Lutz; Nordhausen, Klaus; Schuhmacher, Heike

doi:10.1016/j.jmva.2015.11.009

Cited by 23 publications

(22 citation statements)

References 15 publications

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“…In order to prove differentiability of Σ ρ (·), we need second order Taylor expansions of L ρ (·, Q). These are also useful to replace the fixed-point algorithm described earlier by faster methods, see Dümbgen et al (2013).…”

Section: Second-order Smoothness Of the Criterion Functionmentioning

confidence: 99%

$M$-functionals of multivariate scatter

Duembgen¹,

Pauly²,

Schweizer³

2015

Statist. Surv.

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This survey provides a self-contained account of M -estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying M -functionals and discuss their weak continuity and differentiability. This is done in a rather general framework with matrix-valued random variables. By doing so we reveal a connection between Tyler's (1987a) M -functional of scatter and the estimation of proportional covariance matrices. Moreover, this general framework allows us to treat a new class of scatter estimators, based on symmetrizations of arbitrary order. Finally these results are applied to M -estimation of multivariate location and scatter via multivariate t-distributions.MSC 2010 subject classifications: 62G20, 62G35, 62H12, 62H99.

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Section: Second-order Smoothness Of the Criterion Functionmentioning

confidence: 99%

$M$-functionals of multivariate scatter

Duembgen¹,

Pauly²,

Schweizer³

2015

Statist. Surv.

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“…Actually, they are usually computed using all pairwise differences and computing the original scatter with respect to the origin. Symmetrized M -estimators of scatter are investigated in [17], while the computational issues are especially discussed in [15,18].…”

Section: Definition 5 Let S Denote Any Scatter Functional Then Its Smentioning

confidence: 99%

Non-Gaussian Component Analysis: Testing the Dimension of the Signal Subspace

Radojicic

Nordhausen

2020

Analytical Methods in Statistics

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Dimension reduction is a common strategy in multivariate data analysis which seeks a subspace which contains all interesting features needed for the subsequent analysis. Non-Gaussian component analysis attempts for this purpose to divide the data into a non-Gaussian part, the signal, and a Gaussian part, the noise. We will show that the simultaneous use of two scatter functionals can be used for this purpose and suggest a bootstrap test to test the dimension of the non-Gaussian subspace. Sequential application of the test can then for example be used to estimate the signal dimension.

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“…For more details on M estimators we refer to Dümbgen, Pauly, and Schweizer (2015) and Dümbgen, Nordhausen, and Schuhmacher (2016).…”

Section: Plug-in Estimator For Standard Modelmentioning

confidence: 99%

pvclass: An R Package for p Values for Classification

Zumbrunnen¹,

Dümbgen²

2017

J. Stat. Soft.

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Let (X, Y ) be a random variable consisting of an observed feature vector X and an unobserved class label Y ∈ {1, 2, . . . , L} with unknown joint distribution. In addition, let D be a training data set consisting of n completely observed independent copies of (X, Y ). Instead of providing point predictors (classifiers) for Y , we compute for each b ∈ {1, 2, . . . , L} a p value π b (X, D) for the null hypothesis that Y = b, treating Y temporarily as a fixed parameter, i.e., we construct a prediction region for Y with a certain confidence. The advantages of this approach over more traditional ones are reviewed briefly. In principle, any reasonable classifier can be modified to yield nonparametric p values.We describe the R package pvclass which computes nonparametric p values for the potential class memberships of new observations as well as cross-validated p values for the training data. Additionally, it provides graphical displays and quantitative analyses of the p values.

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New algorithms for M-estimation of multivariate scatter and location

Cited by 23 publications

References 15 publications

$M$-functionals of multivariate scatter

$M$-functionals of multivariate scatter

Non-Gaussian Component Analysis: Testing the Dimension of the Signal Subspace

pvclass: An R Package for p Values for Classification

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