Hungarian Constructions from the Nonasymptotic Viewpoint
Hungarian Constructions from the Nonasymptotic Viewpoint
Let $x_1, \ldots, x_n$ be independent random variables with uniform distribution over $\lbrack 0, 1\rbrack$, defined on a rich enough probability space $\Omega$. Denoting by $\hat{\mathbb{F}}_n$ the empirical distribution function associated with these observations and by $\alpha_n$ the empirical Brownian bridge $\alpha_n(t) = \sqrt n(\hat{\mathbb{F}}_n(t) - t)$, Komlos, Major and …