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An improved bootstrap test of density ratio ordering

Brendan Beare () and Xiaoxia Shi ()

Econometrics and Statistics, 2019, vol. 10, issue C, 9-26

Abstract: Two probability distributions with common support are said to exhibit density ratio ordering when they admit a nonincreasing density ratio. Existing statistical tests of the null hypothesis of density ratio ordering are known to be conservative, with null limiting rejection rates below the nominal significance level whenever the two distributions are unequal. It is shown that a bootstrap procedure can be used to raise the pointwise limiting rejection rate to the nominal significance level on the boundary of the null. This improves power against nearby alternatives. The proposed procedure is based on preliminary estimation of a contact set, the form of which is obtained from a novel representation of the Hadamard directional derivative of the least concave majorant operator. Numerical simulations indicate that improvements to power can be very large in moderately sized samples.

Keywords: Contact set; Density ratio ordering; Hadamard directional differentiability; Least concave majorant; Ordinal dominance curve (search for similar items in EconPapers)
Date: 2019
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Working Paper: An improved bootstrap test of density ratio ordering (2015) Downloads
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