On the calculation of standard error for quotation in confidence statements

Song Chen and Peter Hall

Statistics & Probability Letters, 1994, vol. 19, issue 2, 147-151

Abstract: The variability of a parameter estimator is often expressed by quoting, within parentheses, a value of standard error, say . Typically the latter is calculated via an asymptotic formula, or by application of the bootstrap or jackknife. A common interpretation of the quotation "()" is that the confidence interval I = ( - 2, covers the true value of [theta] with probability approximately 0.95. However, in problems where the allowable range of [theta] is sharply restricted by the context it is sometimes the case that one or other of the endpoints of I lies outside the allowable range. This happens because information about the allowable range is not adequately taken into account when computing the standard error. Examples include confidence statements about ratios of means. In the present paper we suggest a remedy for this problem. We propose a new, symmetrized version of Owen's empirical likelihood method, and use it to construct range-respecting, symmetric confidence intervals. These intervals suggest new formulae for standard error. An alternative approach may be based on a version of the bootstrap, although the latter is more expensive in computing time.

Keywords: Bootstrap; confidence; interval; coverage; empirical; likelihood; range; respecting; standard; error (search for similar items in EconPapers)
Date: 1994
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(94)90148-1
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:19:y:1994:i:2:p:147-151

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 ().