On Strong Approximation of the Multidimensional Empirical Process
On Strong Approximation of the Multidimensional Empirical Process
Let $\mathbf{X}_1, \mathbf{X}_2, \cdots$ be a sequence of i.i.d. rv's uniformly distributed over the unit square $I^2$. Further, let $F_n$ be the empirical distribution function based on the sample $\mathbf{X}_1, \mathbf{X}_2, \cdots, \mathbf{X}_n$. A sequence $\{B_n\}$ of Brownian bridges and a Kiefer process $K$ is constructed such that $$\sup_{A\in Q} …