On symmetric semiparametric two‐sample problem

Moming Li, Guoqing Diao and Jing Qin

Biometrics, 2020, vol. 76, issue 4, 1216-1228

Abstract: We consider a two‐sample problem where data come from symmetric distributions. Usual two‐sample data with only magnitudes recorded, arising from case‐control studies or logistic discriminant analyses, may constitute a symmetric two‐sample problem. We propose a semiparametric model such that, in addition to symmetry, the log ratio of two unknown density functions is modeled in a known parametric form. The new semiparametric model, tailor‐made for symmetric two‐sample data, can also be viewed as a biased sampling model subject to symmetric constraint. A maximum empirical likelihood estimation approach is adopted to estimate the unknown model parameters, and the corresponding profile empirical likelihood ratio test is utilized to perform hypothesis testing regarding the two population distributions. Symmetry, however, comes with irregularity. It is shown that, under the null hypothesis of equal symmetric distributions, the maximum empirical likelihood estimator has degenerate Fisher information, and the test statistic has a mixture of χ2‐type asymptotic distribution. Extensive simulation studies have been conducted to demonstrate promising statistical powers under correct and misspecified models. We apply the proposed methods to two real examples.

Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/biom.13233

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:bla:biomet:v:76:y:2020:i:4:p:1216-1228

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0006-341X

Access Statistics for this article

More articles in Biometrics from The International Biometric Society
Bibliographic data for series maintained by Wiley Content Delivery ().