Optimal tests for multivariate location based on interdirections and pseudo-Mahalanobis ranks

By Marc Hallin, Davy Paindaveine. 2002

146 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/01c695142ba4e191a735b753b711118d2f1a0894

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In Statistics and Probability

Citations in the corpus

Optimal procedures based on interdirections and pseudo-Mahalanobis ranks for testing multivariate elliptic white noise against ARMA dependence (2002, methodology): “Note that the scatter matrix Σ in (1) needs not be (a multiple of) the covariance matrix of the observations, which may not exist, and that f is not, strictly speaking, a probability density; see Hallin and Paindaveine (2002) for a discussion.”
SEMIPARAMETRICALLY EFFICIENT RANK-BASED INFERENCE FOR SHAPE I. OPTIMAL RANK-BASED TESTS FOR SPHERICITY (2006, methodology): “metric location experiment E (n) g := {P θ,σ 2,V;g1 |θ ∈ Rk}, provided that it is ULAN, which essentially requires g1 to satisfy Assumption (A1) (see [17]).”
Nonparametric multivariate rank tests and their unbiasedness (2012, methodology): “In this context, we should mention the papers by Chaudhuri and Sengupta [5], Choi and Marden [6, 7], Hallin and Pandaveine [13], Hetmansperger et al. [17], Liu [21, 23], Liu and Singh [24], Oja and Randles [31], Oja et al. [30], Puri and Sen [33], Randles and Peters [34], Topchii et al. [40], Tukey ”
On the Breakdown Properties of Some Multivariate M‐Functionals * (2005, methodology): “More recently, it has been applied in the development of non- parametric multivariate methods, see e.g. Randles (2000), Hallin & Paindaveine (2002a, 2002b) and Hettmansperger & Randles (2003).”
On Directional Regression for Dimension Reduction (2007, background): “The ( n 2 ) interdirections can be used to estimate the angles between any two points, leading to a multivariate and affine-invariant generalization of the sign test (see, e.g., Randles 1989; Hettmansperger and Oja 1994; Oja 1999; Hallin and Paindaveine 2002, 2005).”
Distribution-Free Consistent Independence Tests via Center-Outward Ranks and Signs (2019, background): “None of them, however, is distributionfree except for pseudo-Mahalanobis ranks (Hallin and Paindaveine 2002a, 2002b), but these are restricted to the class of elliptically symmetric distributions (Fang, Kotz, and Ng 1990).”
Rank-based optimal tests of the adequacy of an elliptic VARMA model (2004, methodology): “The AREs for the fixed-score procedures obtained in Proposition 8 coincide with those obtained in Hallin and Paindaveine (2002b) for the related problem of testing randomness against VARMA dependence.”
ECA: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions (2013, background): “yler (1987), Taskinen et al. (2003), Oja and Randles (2004), Oja and Paindaveine (2005), Oja et al. (2006), and Sirkia et al. (2007). Their theoretical performance in low dimensions were analyzed in Hallin and Paindaveine (2002b,a, 2004, 2005, 2006) and Hallin et al. (2006). Though signicant progres”
OPTIMAL RANK-BASED TESTING FOR PRINCIPAL COMPONENTS (2010, methodology): “LAN (actually, ULAN) has been established, under appropriate regularity assumptions on radial densities, in Hallin and Paindaveine (2006a), for elliptical families when parametrized by a location vector θ and a scatter matrix Σ [more precisely, the vector vech(Σ) resulting from stacking the upper di”
Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach (2021, methodology): “There, they have been used, quite successfully, in a variety of multivariate models, including one-sample location (Hallin and Paindaveine 2002a), k-sample location (Um and Randles 1998), serial dependence (Hallin and Paindaveine 2002b), linear models with VARMA errors (Hallin and Paindaveine…”
Multivariate Nonparametric Tests (2004, methodology): “Optimal signed-rank testing procedures based on interdirections and (univariate) ranks of the lengths of the residual vectors were developed by Hallin and Paindaveine (2002).”
SEMIPARAMETRICALLY EFFICIENT RANK-BASED INFERENCE FOR SHAPE II. OPTIMAL R-ESTIMATION OF SHAPE (2006, unknown): “In such a context, robust inference methods, resisting arbitrarily heavy radial tails, are highly desirable and distribution-free rank-based methods naturally come into the picture (see [9, 10, 11, 12] for closely related results).”
Affine-invariant aligned rank tests for the multivariate general linear model with VARMA errors (2005, methodology): “…relative efficiencies of the proposed procedures with respect to the parametric Gaussian procedure are convex linear combinations of the corresponding asymptotic relative efficiencies in the pure location and purely serial models (see Hallin and Paindaveine 2002a and 2002b, respectively).”