On a transformation and re-transformation technique for constructing an affine equivariant multivariate median-Reference-Cited by-同舟云学术

On a transformation and re-transformation technique for constructing an affine equivariant multivariate median

Published:1996 Issue:8 Volume:124 Page:2539-2547
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Chakraborty Biman,Chaudhuri Probal

Abstract

An affine equivariant version of multivariate median is introduced. The proposed median is easy to compute and has some appealing geometric features that are related to the configuration of a multivariate data cloud. The transformation and re-transformation approach used in the construction of the median has some fundamental connection with the data driven co-ordinate system considered by Chaudhuri and Sengupta (1993, Journal of the American Statistical Association). Large sample statistical properties of the median are discussed and finite sample performance is investigated using Monte Carlo simulations.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1996-124-08/S0002-9939-96-03657-X/S0002-9939-96-03657-X.pdf

Reference17 articles.

1. Note on the spatial quantile of a random vector;Abdous, B.;Statist. Probab. Lett.,1992

2. Arcones, M.A., Chen, Z. and Giné, E. (1994), Estimators related to U-processes with applications to multivariate medians : Asymptotic normality. The Annals of Statistics, 22, 1460–1477.

3. Joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population;Babu, G. Jogesh;J. Multivariate Anal.,1988

4. A note on quantiles in large samples;Bahadur, R. R.;Ann. Math. Statist.,1966

5. The ordering of multivariate data;Barnett, V.;J. Roy. Statist. Soc. Ser. A,1976

Cited by 40 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the use of robust estimators of multivariate location for heterogeneous data;Statistics & Probability Letters;2023-12

2. An integrated local depth measure;AStA Advances in Statistical Analysis;2022-01-03

3. Bayesian Inference on Multivariate Medians and Quantiles;Statistica Sinica;2022

4. Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach;The Annals of Statistics;2021-04-01

5. The Convex-Hull-Stripping Median Approximates Affine Curvature Motion;Lecture Notes in Computer Science;2019