Uniform strong consistency of sample quantiles

Ryszard Zielinski

Statistics & Probability Letters, 1998, vol. 37, issue 2, 115-119

Abstract: It is well known that if xq(F) is the unique qth quantile of a distribution function F, then Xk(n):n with k(n)/n --> q is a strongly consistent estimator of xq(F). However, for every [var epsilon] >0 and for every, even very large n, supF[set membership, variant]F,PF{Xk(n):n--Xq(F)>[var epsilon]}=1. This is a consequence of the fact that in the family of all distribution functions with uniquely defined qth quantile the almost sure convergence Xk(n):n --> xq(F) is not uniform. A simple necessary and sufficient condition for the uniform strong consistency of Xk(n):n is given.

Keywords: Uniform; strong; convergence; Sample; quantiles; Nonparametric; model; [var; epsilon]-contamination (search for similar items in EconPapers)
Date: 1998
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(97)00108-9
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:37:y:1998:i:2:p:115-119

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().