A simultaneous confidence-bounded true discovery proportion perspective on localizing differences in smooth terms in regression models

David Swanson

Computational Statistics & Data Analysis, 2025, vol. 211, issue C

Abstract: A method is demonstrated for localizing where two spline terms, or smooths, differ using a true discovery proportion (TDP)-based interpretation. The procedure yields a statement on the proportion of some region where true differences exist between two smooths. The methodology avoids ad hoc approaches to making such statements, like subsetting the data and performing hypothesis tests on the truncated spline terms. TDP estimates are 1-α confidence-bounded simultaneously, which means that a region's TDP estimate is a lower bound on the proportion of actual differences, or true discoveries, in that region, with high confidence regardless of the number of estimates made. The procedure is based on closed-testing using Simes local test. This local test requires that the multivariate χ2 test statistics of generalized Wishart type underlying the method be positive regression dependent on subsets (PRDS), a result for which evidence is presented suggesting that the condition holds. Consistency of the procedure is demonstrated for generalized additive models with the tuning parameter chosen by REML or GCV, and the achievement of confidence-bounded TDP is shown in simulation as is an analysis of walking gait.

Keywords: Splines; Smoothing; Multiple testing; Closed-testing; Simultaneous confidence (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947325000738
Full text for ScienceDirect subscribers only.

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:eee:csdana:v:211:y:2025:i:c:s0167947325000738

DOI: 10.1016/j.csda.2025.108197

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().