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arXiv · 2011.10965

Least favorability of the uniform distribution for tests of the concavity of a distribution function

Brendan K. Beare
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Abstract

A test of the concavity of a distribution function with support contained in the unit interval may be based on a statistic constructed from the $L^p$-norm of the difference between an empirical distribution function and its least concave majorant. It is shown here that the uniform distribution is least favorable for such a test, in the sense that the limiting distribution of the statistic obtained under uniformity stochastically dominates the limiting distribution obtained under any other concave distribution function.

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Brendan K. Beare. 2020-11-22. Least favorability of the uniform distribution for tests of the concavity of a distribution function. https://doi.org/10.1002/sta4.376

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