I want to know How to calculate Laplace transform of $Y^2-1$.
I'm posting a question because I want to know that part and the middle part omitted from the proof in more detail.
Lastly, please tell me how Corollary of Lemma 1 was induced and the math subjects I need to understand the proof.
Thank you.
Paper : ADAPTIVE ESTIMATION OF A QUADRATIC FUNCTIONAL BY MODEL SELECTION, The Annals of Statistics, 2000