Chernoff's Density Is Strongly Log-Concave

2026/07/21 by Xianyang Zhang, Quan Zhou
#math.PR #math.ST #stat.TH

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Abstract

Let f be the density of the Chernoff random variable argmax_t∈ℝ\W(t)-t²\, where W is a two-sided Brownian motion. This note proves the conjecture of Balabdaoui and Wellner (2014) that f is strongly log-concave. The proof was generated in its entirety by GPT-5.6 Sol.

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