tortue

I want to pose this question as general as possible and ask for reference of what to do in similar situations. I'll incrementally add details to narrow down the problem. I want to derive large deviation bound for $\| X + Y \|_2^2$, where $X$ and $Y$ are $p$-dimensional dependent vectors; I b...

Let $\mathbf{R} \ni X_1, \dots, X_n \sim \mathcal{N}(0, \sigma^2)$. I can show that $$ \mathbb{E} ~ \text{Med} \{X_1, \dots, X_n\} = 0 $$ and want to compute the variance of the same sample median, i.e. $$ \mathbb{V}ar ~ \text{Med} \{X_1, \dots, X_n\} $$ I have a guess that it should behave l...