Inference on the shape of elliptical distributions based on the MCD

Davy Paindaveine, Germain Van Bever

Research output: Contribution to journalArticle

Abstract

The minimum covariance determinant (MCD) estimator of scatter is one of the most famous robust procedures for multivariate scatter. Despite the quite important research activity related to this estimator, culminating in the recent thorough asymptotic study ofCator and Lopuhaä (2010, 2012), no results have been obtained on the corresponding estimator of shape, which is the parameter of interest in many multivariate problems (including principal component analysis, canonical correlation analysis, testing for sphericity, etc.) In this paper, we therefore propose and study MCD-based inference procedures for shape, that inherit the good robustness properties of the MCD. The main emphasis is on asymptotic results, for point estimation (Bahadur representation and asymptotic normality results) as well as for hypothesis testing (asymptotic distributions under the null and under local alternatives). Influence functions of the MCD-estimators of shape are obtained as a corollary. Monte-Carlo studies illustrate our asymptotic results and assess the robustness of the proposed procedures.

Original languageEnglish
Pages (from-to)125-144
Number of pages20
JournalJournal of Multivariate Analysis
Volume129
DOIs
Publication statusPublished - 2014
Externally publishedYes

Fingerprint

Minimum Covariance Determinant
Elliptical Distribution
Estimator
Testing
Scatter
Principal component analysis
Bahadur Representation
Robustness
Sphericity
Canonical Correlation Analysis
Local Alternatives
Point Estimation
Influence Function
Monte Carlo Study
Hypothesis Testing
Asymptotic Normality
Principal Component Analysis
Asymptotic distribution
Null
Corollary

Keywords

  • Bahadur representation results
  • Elliptical distributions
  • MCD estimators
  • Robustness
  • Shape parameters
  • Tests of sphericity

Cite this

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Inference on the shape of elliptical distributions based on the MCD. / Paindaveine, Davy; Van Bever, Germain.

In: Journal of Multivariate Analysis, Vol. 129, 2014, p. 125-144.

Research output: Contribution to journalArticle

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T1 - Inference on the shape of elliptical distributions based on the MCD

AU - Paindaveine, Davy

AU - Van Bever, Germain

PY - 2014

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