Maximum likelihood estimation of two-sample population proportions under constraint on their difference

Shubhabrata Das

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 9, 2836-2851

Abstract: We derive the maximum likelihood estimate (MLE) of a population proportion when it differs from the same of a second population by a known value. This constrained MLE (CMLE) has a closed form in limited scenarios, which are completely characterized. These include the cases when the CMLE takes a boundary value in the parameter space. The existence of solution is established in the other cases and numerical methods are adopted in R and Excel to obtain the estimates solving a nonlinear equation. The standard error of the CMLE is estimated via bootstrap which also yields a confidence interval estimate; this is compared with a second method based on asymptotic distribution. The CMLE is of particular importance in the two sample testing of hypothesis of proportions based on independent samples, when these parameters differ by a non-zero value under the null hypothesis. Numerical computation establishes that the test statistic using the standard error based on this CMLE leads to a more reliable decision than the existing alternatives when the sample sizes are moderate to large.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2021.1961152 (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:lstaxx:v:52:y:2023:i:9:p:2836-2851

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2021.1961152

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().