4 problems

Let $Y_1,\ldots,Y_n$ be independent identically distributed samples from a Gaussian distribution, let $\mathbf{y}=(Y_1,\ldots,Y_n)$, let $\bar{\mathbf{y}}$ be their sample mean, an…

Let $\mathbf{W}^{(n)}=\mathrm{W}_2^2(\hat\mu^{1,(n)},\hat\nu^{1,(n)})$ be the squared Wasserstein distance between two empirical samples of size $n$ from the standard normal distri…

Conjecture on improving the Poisson approximation bound. The order of the upper bound in the displayed inequality can be significantly improved.

Let $p$ be a positive integer and let $W=\sum_{i\in I}X_i$, where ${\mathbbm{E}}X_i=0$, ${\mathbbm{E}}W^2=1$, and the variables satisfy (LD1)--(LD$(p+1)$): for each $i_1\in I$,…