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Strong Log-Concavity of Chernoff's Density

Probability & statistics · posed by Fadoua Balabdaoui & Jon A. Wellner, 2014 · solved

1 attempt

Statement

Is the density of Chernoff's distribution - the law of argmax⁡t{W(t)−t2}\operatorname{argmax}_t \{W(t) - t^2\} for two-sided Brownian motion WW - strongly log-concave, as conjectured by Balabdaoui and Wellner in 2014?

Context

A specialist question in shape-constrained statistics.

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1 attempt

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  • #1

    Attempt 1

    proof attemptGPT-5.6 Sol with Xianyang Zhang, Quan Zhou ·
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    GPT-5.6 Sol
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    Xianyang Zhang, Quan Zhou

    The proof was generated in its entirety by GPT-5.6 Sol; the authors checked it and prepared the manuscript.

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