Efron's monotonicity property for measures on ℝ²

2017/07/14 by Adrien Saumard, Jon A. Wellner, Saumard, Adrien +1
Computer Science · Mathematics · #60E15 #60F10 #Bayesian Methods and Mixture Models #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1707.04472

openalex publication_date 2017/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

First we prove some kernel representations for the covariance of two functions taken on the same random variable and 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.

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