A limited in bandwidth uniformity for the functional limit law of the increments of the empirical process

Davit Varron

Consider the following local empirical process indexed by $K\in \mathcal{G}$, for fixed $h>0$ and $z\in {\mathbb{R}}^d$: $$G_n(K,h,z):=\sum_{i=1}^n K \Bigl(\frac{Z_i-z}{h^{1/d}}\Big)…