Inequality for square of the subgaussian distributions
For my research I am trying to bound some exponential moments of subgaussian r.v.’s. And I am stuck with proving one of such inequalities. More specifically:
Let be unit vector in and , , be i.i.d *Rademacher* rv’s. Also let . I know that , where is standard normal r.v. and independent of ’s.
Now my question is: would this inequality also works if we change the sign on ? i.e.:
I have run many numerical experiments and it seems to be correct, but I am yet to prove it.
What I have done so far is as follows:
but I am stuck here (not even sure if what I have done is going to get me anywhere at all). This must be something that someone out there should know about, I am hoping.
Any help, suggestion or pointers would be greatly appreciate it.
Cheers and thanks for reading
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