7 problems

Combinatorial-dimension conjecture. For every uniformly bounded class $F$,

Let $F$ be the distribution function of the transformed observations, let $\hat F_n$ be the empirical distribution function based on the rank-based pseudo-observations, and define…

Let $\mathcal{X} \subseteq \mathbb{R}^d$, let $\nu$ have a density, and let $P$ and $Q$ be measures on $\mathcal{X}$ with densities bounded away from zero, satisfying…

Norm-comparison conjecture. One has

Glivenko–Cantelli conjecture. The empirical fractions satisfy

Let $(X_i)_{i\leq N}$ be independent identically distributed random variables and let ${\cal F}$ be a countable class of measurable functions. Define … and let $d_p(f,g)=\|f-g\|_p$…

Error-density estimation conjecture. For each fixed $x$,