EconPapers    
Economics at your fingertips  
 

On the lengths of t-based confidence intervals

Yu Zhang and Xiangzhong Fang

Journal of Applied Statistics, 2021, vol. 48, issue 6, 993-1008

Abstract: Confidence interval is a basic type of interval estimation in statistics. When dealing with samples from a normal population with the unknown mean and the variance, the traditional method to construct t-based confidence intervals for the mean parameter is to treat the n sampled units as n groups and build the intervals. Here we propose a generalized method. We first divide them into several equal-sized groups and then calculate the confidence intervals with the mean values of these groups. If we define “better” in terms of the expected length of the confidence interval, then the first method is better because the expected length of the confidence interval obtained from the first method is shorter. We prove this intuition theoretically. We also specify when the elements in each group are correlated, the first method is invalid, while the second can give us correct results in terms of the coverage probability. We illustrate this with analytical expressions. In practice, when the data set is extremely large and distributed in several data centers, the second method is a good tool to get confidence intervals, in both independent and correlated cases. Some simulations and real data analyses are presented to verify our theoretical results.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/02664763.2020.1754357 (text/html)
Access to full text is restricted to subscribers.

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:taf:japsta:v:48:y:2021:i:6:p:993-1008

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/CJAS20

DOI: 10.1080/02664763.2020.1754357

Access Statistics for this article

Journal of Applied Statistics is currently edited by Robert Aykroyd

More articles in Journal of Applied Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().

 
Page updated 2025-03-20
Handle: RePEc:taf:japsta:v:48:y:2021:i:6:p:993-1008