Equivalence of Regression Curves

Holger Dette, Kathrin Möllenhoff, Stanislav Volgushev and Frank Bretz

Journal of the American Statistical Association, 2018, vol. 113, issue 522, 711-729

Abstract: This article investigates the problem whether the difference between two parametric models m1, m2 describing the relation between a response variable and several covariates in two different groups is practically irrelevant, such that inference can be performed on the basis of the pooled sample. Statistical methodology is developed to test the hypotheses H0: d(m1, m2) ⩾ ϵ versus H1: d(m1, m2) < ϵ to demonstrate equivalence between the two regression curves m1, m2 for a prespecified threshold ϵ, where d denotes a distance measuring the distance between m1 and m2. Our approach is based on the asymptotic properties of a suitable estimator d(m^1,m^2)$d(\hat{m}_1, \hat{m}_2)$ of this distance. To improve the approximation of the nominal level for small sample sizes, a bootstrap test is developed, which addresses the specific form of the interval hypotheses. In particular, data have to be generated under the null hypothesis, which implicitly defines a manifold for the parameter vector. The results are illustrated by means of a simulation study and a data example. It is demonstrated that the new methods substantially improve currently available approaches with respect to power and approximation of the nominal level.

Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2017.1281813 (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:jnlasa:v:113:y:2018:i:522:p:711-729

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2017.1281813

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().