Electronic Journal of Statistics

Asymptotic hypotheses testing for the colour blind problem

Laura Dumitrescu and Estate V. Khmaladze

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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.

Article information

Electron. J. Statist., Volume 13, Number 2 (2019), 4573-4595.

Received: March 2019
First available in Project Euclid: 12 November 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties

Asymptotically optimal test contiguous alternatives dependence alternatives empirical process goodness of fit Kolmogorov–Smirnov statistics unordered pairs

Creative Commons Attribution 4.0 International License.


Dumitrescu, Laura; Khmaladze, Estate V. Asymptotic hypotheses testing for the colour blind problem. Electron. J. Statist. 13 (2019), no. 2, 4573--4595. doi:10.1214/19-EJS1634. https://projecteuclid.org/euclid.ejs/1573527691

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