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2019 Asymptotic hypotheses testing for the colour blind problem
Laura Dumitrescu, Estate V. Khmaladze
Electron. J. Statist. 13(2): 4573-4595 (2019). DOI: 10.1214/19-EJS1634


Within a nonparametric framework, we consider the problem of testing the equality of marginal distributions for a sequence of independent and identically distributed bivariate data, with unobservable order in each pair. In this case, it is not possible to construct the corresponding empirical distributions functions and yet this article shows that a systematic approach to hypothesis testing is possible and provides an empirical process on which inference can be based. Furthermore, we identify the linear statistics that are asymptotically optimal for testing the hypothesis of equal marginal distributions against contiguous alternatives. Finally, we exhibit an interesting property of the proposed stochastic process: local alternatives of dependence can also be detected.


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Laura Dumitrescu. Estate V. Khmaladze. "Asymptotic hypotheses testing for the colour blind problem." Electron. J. Statist. 13 (2) 4573 - 4595, 2019.


Received: 1 March 2019; Published: 2019
First available in Project Euclid: 12 November 2019

zbMATH: 07136625
MathSciNet: MR4029803
Digital Object Identifier: 10.1214/19-EJS1634

Primary: 62G10
Secondary: 62G20

Keywords: asymptotically optimal test , contiguous alternatives , dependence alternatives , empirical process , goodness of fit , Kolmogorov–Smirnov statistics , unordered pairs


Vol.13 • No. 2 • 2019
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