Efron’s monotonicity property for measures on R2

Adrien Saumard and Jon A. Wellner

Journal of Multivariate Analysis, 2018, vol. 166, issue C, 212-224

Abstract: In this paper, we prove some kernel representations for the covariance of two functions taken on the same random variable and we deduce kernel representations for some functionals of a continuous one-dimensional measure. Then we apply these formulas to extend Efron’s monotonicity property, given in Efron (1965) and valid for independent log-concave measures, to the case of general measures on R2. The new formulas are also used to derive some further quantitative estimates in Efron’s monotonicity property.

Keywords: Covariance identity; Log-concave; Functional inequality; Monotonicity; Measurement error (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.jmva.2018.03.005

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