Permutation tests for multivariate order-constrained testing problems

Abstract

This article discusses an effective permutation-based approach to solve order-constrained testing problems, which are very difficult or even impossible to solve within the framework of parametric likelihood. The nonparametric combination (NPC) methodology is a flexible tool which relies on dependent permutation tests and allows us to deal with a large variety of complex testing problems, including the stochastic dominance and monotonic stochastic ordering problems of interest. To deal with them in line with Roy’s Union-Intersection (UI) approach, the NPC procedure decomposes the original hypothesis into suitable sub-hypotheses. In this article we discuss and compare two possible types of decomposition, exploiting an extensive simulation study. A real data application is also proposed, in which multivariate ordinal data from the medical field are analyzed.

Keywords:

• Monotonic stochastic ordering
• Nonparametric combination
• Stochastic dominance
• Union-intersection

Acknowledgement

The authors would like to express their thanks to three referees and the Editor for accurate reading, criticisms and suggestions that have contributed to improve our paper.

This study was carried out within:

• the MOST—Sustainable Mobility National Research Center and received funding from the European Union Next-GenerationEU (Piano Nazionale di Ripresa e Resilienza (PNRR)—Missione 4 Componente 2, Investimento 1.4—D.D. 1033 17 June 2022, CN00000023). This manuscript reflects only the authors’ views and opinions, neither the European Union nor the European Commission can be considered responsible for them.

• the MICS (Made in Italy – Circular and Sustainable) Extended Partnership and received funding from Next-Generation EU (Italian PNRR – M4 C2, Invest 1.3 – D.D. 1551.11-10-2022, PE00000004). CUP MICS C93C220052800.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by Guangzhou University and the University of Padova.