A practical affine equivariant multivariate median

By Thomas P. Hettmansperger, Ronald H. Randles. 2002

173 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/58ae5a83ba98177ab33647d8264b9778f22b87b5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

Elliptical graphical modelling (2011, background): “Here μ̂n is an appropriate location estimator, which may be the mean, or, in light of robustness, the Hettmansperger-Randles median (Hettmansperger and Randles, 2002). Existence and uniqueness of a solution of (5.19) and the asymptotic properties of the estimator T̂n are treated in the original publ”
Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices (2006, background): “Tyler's M estimate has a low breakdown point, but is very fast to compute (see Hettmansperger and Randles, 2002 ), and has good efficiency in larger dimensions.”
Sign test of independence between two random vectors (2003, methodology): “In Hettmansperger and Randles (2002) estimates µ̂ and V̂ are obtained as follows.”
Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem (2016, methodology): “11.3) Q2n = p 2∑ i=1 niÛTi Ûi, (2) where Ûi = n−1i ∑ni j=1 Ûi j, Ûi j = U (S−1/2(Xi j − θ̂)), θ̂ and S−1/2 are Hettmansperger and Randles (2002) estimates (HRE) of location and scatter matrix so that 2∑ i=1 ni∑ j=1 Ûi j = 0 and pn−1 2∑ i=1 ni∑ j=1 Ûi jÛTi j = Ip.”
SEMIPARAMETRICALLY EFFICIENT RANK-BASED INFERENCE FOR SHAPE II. OPTIMAL R-ESTIMATION OF SHAPE (2006, unknown): “(2.2) Although any root-n consistent estimator θ̂ could be used, we suggest adopting the multivariate affine-equivariant median introduced by Hettmansperger and Randles [18] which is itself a “sign-based” estimator.”
Symmetrised M-estimators of multivariate scatter (2007, background): “Previously proposed algorithms either have restrictions on the weight functions or do not have rigorous proofs of convergence, see Hettmansperger and Randles [6].”
OPTIMAL RANK-BASED TESTING FOR PRINCIPAL COMPONENTS (2010, methodology): “Denote by θ̂HR the Hettmansperger and Randles (2002) affine-equivariant median, and by V̂Tyler the shape estimator of Tyler (1987), normalized so that it has determinant one: both are root-n consistent under any radial density g1.”
Multivariate Nonparametric Tests of Independence (2005, background): “Here the observations are centered on some affineequivariant location estimator µ̂ (1) based on x(1)1 , . . . ,x (1) n , for example, the Oja (1983) median or the transformationretransformation spatial median (Hettmansperger and Randles 2002).”
Sign and Rank Covariance Matrices: Statistical Properties and Application to Principal Components Analysis (2002, background): “Tyler’s scatter matrix estimate Hettmansperger and Randles [3] discussed location and scatter estimate based on spatial signs, but now resulting in an affine equivariant procedure.”
Multivariate Nonparametric Tests (2004, methodology): “A multivariate median estimating a directional center of the population and corresponding to the sign test based onQ2 in the Hodges–Lehmann sense was developed by Hettmansperger and Randles (2002).”