Talk:Bretagnolle–Huber inequality

Tsybakov's book
I have tried to verify the proof steps from Tsybakov's cited book, which I have in my library; however, I am unable even to find the name. It seems to me that the statement here is basically Lemma 2.6 in the book, but although it is credited to Bretagnolle and Huber in the historical notes, it is not given a name of its own. Could you help clear this up? Felix QW (talk) 10:39, 20 August 2022 (UTC)


 * Hi @Felix QW, Thanks a lot for having an in-depth look at the proofs. In my edition, it is Lemma 2.6 page 89 of Tsybakov's book, I will add the precise reference. Note that the short note by Clement Canonne 2022 that I cite also reproduces the exact argument of Tsybakov and is slightly easier to read in my opinion. Hope this helps, let me know if you have more questions. ClaireVern (talk) 09:20, 22 August 2022 (UTC)
 * Excellent, so we have the same edition! The issue I had now was more with the claim that the name "Bretagnolle-Huber Inequality" is due to Tsybakov, given that the lemma is not labelled in the text itself (thanks for adding the exact reference, that really helps). Felix QW (talk) 09:34, 22 August 2022 (UTC)
 * I see, I found the lemma by doing a ctrl+F search for "Bretagnolle", which led me to this statement in the bibliography notes (page 133) "Assouad’s lemma appeared in Assouad (1983). In a slightly less general form it is given in the paper of Bretagnolle and Huber (1979) which contains already the main idea of the construction". My understanding is that Alexandre Tsybakov being francophone, he was the first to extract this lemma from the typewritter proceedings of the "Seminaire de Probabilites de Strasbourg". I am however, not very strongly feeling about these naming credit questions (and I doubt Tsybakov is much either, from my encounters with him). I will soften the phrasing. ClaireVern (talk) 11:34, 26 August 2022 (UTC)

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