Abstract
We show that the density of $Z=\mathop{\operatorname{argmax}}\{W(t)-t^{2}\}$, sometimes known as Chernoff’s density, is log-concave. We conjecture that Chernoff’s density is strongly log-concave or “super-Gaussian”, and provide evidence in support of the conjecture.
Citation
Fadoua Balabdaoui. Jon A. Wellner. "Chernoff’s density is log-concave." Bernoulli 20 (1) 231 - 244, February 2014. https://doi.org/10.3150/12-BEJ483
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