Identifying shifts between two regression curves

Holger Dette (), Subhra Sankar Dhar () and Weichi Wu ()
Additional contact information
Holger Dette: Ruhr-Universität Bochum
Subhra Sankar Dhar: IIT Kanpur
Weichi Wu: Tsinghua University

Annals of the Institute of Statistical Mathematics, 2021, vol. 73, issue 5, No 1, 855-889

Abstract: Abstract This article studies the problem whether two convex (concave) regression functions modelling the relation between a response and covariate in two samples differ by a shift in the horizontal and/or vertical axis. We consider a nonparametric situation assuming only smoothness of the regression functions. A graphical tool based on the derivatives of the regression functions and their inverses is proposed to answer this question and studied in several examples. We also formalize this question in a corresponding hypothesis and develop a statistical test. The asymptotic properties of the corresponding test statistic are investigated under the null hypothesis and local alternatives. In contrast to most of the literature on comparing shape invariant models, which requires independent data the procedure is applicable for dependent and non-stationary data. We also illustrate the finite sample properties of the new test by means of a small simulation study and two real data examples.

Keywords: Comparison of curves; Nonparametric regression; Hypothesis testing (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10463-020-00771-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:aistmt:v:73:y:2021:i:5:d:10.1007_s10463-020-00771-2

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-020-00771-2

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().