According to He et al. (2016), the log-likelihood of Poisson models, $$ L (\beta) = \sum_{i} - \log(x_{i}^{\mathsf{T}}\beta) + y_{i}x_{i}^{\mathsf{T}}\beta - \log y_{i}! $$ for a random variable, $y_{i} \sim \text{Pois}(x_{i}^\mathsf{T}\beta) $, is "known to be non-globally Lipschitz continuous or differentiable" (p. 2). Apparently this result is so well-known that it does not require a citation. Does anyone know where this was shown?
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2(If you are going to criticise lack of citation, make sure you give page numbers for your own citations.) I have edited your question to add this. ; ) – Ben Jun 01 '20 at 01:17
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Alright, thanks. The same statement actually appears in the abstract, too. – Durden Jun 01 '20 at 01:37