Note on Qualitative Robustness of Multivariate Sample Mean and Median
Joint Authors
Gordienko, Evgueni
Novikov, Andrey
Ruiz de Chávez, J.
Source
Journal of Probability and Statistics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-02-17
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
It is known that the robustness properties of estimators depend on the choice of a metric in the space of distributions.
We introduce a version of Hampel's qualitative robustness that takes into account the n-asymptotic normality of estimators in Rk, and examine such robustness of two standard location estimators in ℝk.
For this purpose, we use certain combination of the Kantorovich and Zolotarev metrics rather than the usual Prokhorov type metric.
This choice of the metric is explained by an intention to expose a (theoretical) situation where the robustness properties of sample mean and L1-sample median are in reverse to the usual ones.
Using the mentioned probability metrics we show the qualitative robustness of the sample multivariate mean and prove the inequality which provides a quantitative measure of robustness.
On the other hand, we show that L1-sample median could not be “qualitatively robust” with respect to the same distance between the distributions.
American Psychological Association (APA)
Gordienko, Evgueni& Novikov, Andrey& Ruiz de Chávez, J.. 2013. Note on Qualitative Robustness of Multivariate Sample Mean and Median. Journal of Probability and Statistics،Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-454695
Modern Language Association (MLA)
Gordienko, Evgueni…[et al.]. Note on Qualitative Robustness of Multivariate Sample Mean and Median. Journal of Probability and Statistics No. 2013 (2013), pp.1-8.
https://search.emarefa.net/detail/BIM-454695
American Medical Association (AMA)
Gordienko, Evgueni& Novikov, Andrey& Ruiz de Chávez, J.. Note on Qualitative Robustness of Multivariate Sample Mean and Median. Journal of Probability and Statistics. 2013. Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-454695
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-454695