Edgeworth expansions for studentized and prepivoted sample quantiles

Michael Falk and Daniel Janas

Statistics & Probability Letters, 1992, vol. 14, issue 1, 13-24

Abstract: Edgeworth expansions of length two are established for the sample quantile, preprivoted by a smoothed bootstrap, and for a studentized sample quantile, where we studentize by means of a kernel density estimate. As a consequence, it turns out that that two-sides confidence intervals for the underlying quantile which are based on these approaches have essentially equal coverage probabilities with level errors being of order o(n-), where n is the sample size. The smoothed bootstrap therefore outperforms competitors such as the percentile method or sign test method which have level errors only of order O(n-). In case of one-sided confidence intervals, the smoothed bootstrap is superior to studentization if and only if the derivative of the underlying density at the quantile is positive. Ams 1980 Subject Classifications: Primary 62E20; Secondary 62G15

Keywords: Bootstrap; confidence; interval; coverage; error; Edgeworth; expansion; kernel; density; estimator; prepivoting; smoothed; bootstrap (search for similar items in EconPapers)
Date: 1992
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(92)90205-J
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:14:y:1992:i:1:p:13-24

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 ().