On the uniqueness of S-functionals and M-functionals under nonelliptical distributions

By K. Tatsuoka, David E. Tyler. 2000

145 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/25cf5529669154850198b9183ee2acc9fbc82643

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Symmetrised M-estimators of multivariate scatter (2007, background): “Further, Tatsuoka and Tyler [18] and Kent and Tyler [12] considered the uniqueness of different M-functionals under broad class of symmetric distributions.”
Central limit theorem and influence function for the MCD estimators at general multivariate distributions (2009, background): “The uniqueness of the MCD functional for an f of this kind would be similar to the results in [23] for S- and M -functionals.”
A canonical definition of shape (2008, unknown): “…and Randles (2002), and Randles (2000)), (ii) S(Σ) = (trΣ)/k (Dümbgen (1998), Ollila et al. (2004), and Tyler (1987)), and (iii) S(Σ) = |Σ|1/k (Dümbgen and Tyler (2005), Hallin and Paindaveine (2008a), SalibianBarrera et al. (2006), Taskinen et al. (2006), and Tatsuoka and Tyler (2000)).”
Outlier detection for skewed data (2008, unknown): “the MCD-estimator [2], the Stahel-Donoho estimator [3, 4], S-estimators [5, 6] and MM-estimators [7].”
Robust statistics for outlier detection (2011, background): “More recently, robust estimators of multivariate location and scatter include S -estimators, 2 , 19 MM-estimators, 20 and the orthogonalized Gnanadesikan-Kettenring (OGK) estimator.”
Principal Components Analysis Based on Multivariate MM Estimators With Fast and Robust Bootstrap (2006, methodology): “In particular, we use the eigenvectors and eigenvalues of multivariate MM estimators of shape as introduced by Tatsuoka and Tyler (2000).”
High-Breakdown Robust Multivariate Methods (2008, background): “Recently, Salibian-Barrera, Van Aelst and Willems (2006) proposed using S- or MM-estimators of scatter and developed a fast robust bootstrap procedure for inference and to assess the stability of the PCA solution.”
Invariant co‐ordinate selection (2009, unknown): “…estimates (Maronna et al., 1992; Tyler, 1994), r-estimates (Lopuhaâ, 1991), constrained M-estimates (Kent and Tyler, 1996) and MM estimates (Tatsuoka and Tyler, 2000; Tyler, 2002), as well Address for correspondence: David E. Tyler, Department of Statistics, Rutgers University, 1 10…”