5 problems

Beta-one conjecture. Theorem may apply for a large range of probabilities when $\beta_{m,n}$ is replaced by $1$.

Let samples be drawn from distributions that admit a density and have certain concentration properties. For a sample size $K_S$, let $\hat{P}_{K_S}$ denote the resulting empirical…

Let a $\Psi$-process be a process satisfying the assumptions of Theorem cited in the source, and let its points at time $t$ have an empirical distribution on $[0,1]$. Uniform empir…

Let $P$ be a distribution on a finite alphabet of size $k$, let $\hat{P}_{n,k}$ be its empirical distribution from $n$ independent samples, and let $D(\hat{P}_{n,k} \| P)$ denote t…

Let $P$ be a distribution on a finite alphabet of size $k$, let $\hat{P}_{n,k}$ be its empirical distribution from $n$ independent samples, and let $D(\hat{P}_{n,k} \\| P)$ denote…