On Affine Equivariant Multivariate Quantiles

By Biman Chakraborty. 2001

75 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0393a8fb77e5e6a40d2958bab55e3ba0b947e391

How researchers see this paper

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

In Applied Mathematics

1. Andrea Cerioli
2. Robert Serfling
3. Marc G. Genton
4. Yulia V. Marchenko
5. Mathieu Ribatet
6. A. C. Davison

In Statistics and Probability

1. Yulia V. Marchenko
2. Andrea Cerioli
3. Robert Serfling
4. Marc G. Genton
5. Adelchi Azzalini
6. Reinaldo Boris Arellano-Valle
7. Vytaras Brazauskas
8. Ricardas Zitikis

Citations in the corpus

• Multivariate Outlier Detection With High-Breakdown Estimators (2010, background): “(2) The proportionality constant kMCD(h,n, v), depending on the values of h, n, and v, serves the purpose of making ̂(MCD) both consistent and unbiased when each yi ∼ N(μ, ) (Croux and Haesbroeck 1999; Pison, Van Aelst, and Willems 2002).”
• Multivariate log‐skew‐elliptical distributions with applications to precipitation data (2009, background): “Various definitions of a multivariate quantile have been proposed and studied in the literature (e.g., Chaudhuri, 1996; Chakraborty, 2001).”
• A Depth Function and a Scale Curve Based on Spatial Quantiles (2002, methodology): “Marden (1998) illustrates the use of bivariate QQ-plots based on spatial quantiles, along with some related devices, and similar methods based on a modified type of sample spatial quantile are developed in Chakraborty (2001).”
• Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation (2010, methodology): “…QMS(u, Xn) may be carried out in straightforward fashion by solving −1 n n∑ i=1 S(M(Xn)−1/2(x − Xi )) = u. (33) See Chaudhuri (1996) for discussion with respect to the usual spatial quantiles and Chakraborty (2001) for discussion with respect to the TR spatial quantiles defined by Equation (30).”
• Nonparametric Multivariate Descriptive Measures Based on Spatial Quantiles (2004, methodology): “…analogue of procedures widely used in univariate data analysis, Marden (1998) illustrates the use of bivariate QQ-plots based on spatial quantiles, along with some related devices, and Chakraborty (2001) develops similar methods based on a modified type of sample spatial quantile (discussed below).”