Testing for no effect in regression problems: A permutation approach

Michał G. Ciszewski, Jakob Söhl, Ton Leenen, Bart van Trigt and Geurt Jongbloed

Statistica Neerlandica, 2025, vol. 79, issue 1

Abstract: Often the question arises whether Y can be predicted based on X using a certain model. Especially for highly flexible models such as neural networks one may ask whether a seemingly good prediction is actually better than fitting pure noise or whether it has to be attributed to the flexibility of the model. This paper proposes a rigorous permutation test to assess whether the prediction is better than the prediction of pure noise. The test avoids any sample splitting and is based instead on generating new pairings of (Xi,Yj). It introduces a new formulation of the null hypothesis and rigorous justification for the test, which distinguishes it from the previous literature. The theoretical findings are applied both to simulated data and to sensor data of tennis serves in an experimental context. The simulation study underscores how the available information affects the test. It shows that the less informative the predictors, the lower the probability of rejecting the null hypothesis of fitting pure noise and emphasizes that detecting weaker dependence between variables requires a sufficient sample size.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/stan.12346

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:stanee:v:79:y:2025:i:1:n:e12346

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0039-0402

Access Statistics for this article

Statistica Neerlandica is currently edited by Miroslav Ristic, Marijtje van Duijn and Nan van Geloven

More articles in Statistica Neerlandica from Netherlands Society for Statistics and Operations Research
Bibliographic data for series maintained by Wiley Content Delivery ().