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A limited in bandwidth uniformity for the functional limit law of the increments of the empirical process
Empricial processes Functional limit theorems Strong theorems Density estimation LATEX2ε
2009/9/16
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 (frac{Z_i-z}{h^{1/d}}) - mathbb{E} (K (frac{Z_i-z}{h^{1...
One more approach to the convergence of the empirical process to the Brownian bridge
Empirical process Donsker Theorem Brownian bridge
2009/9/16
A theorem of Donsker asserts that the empirical process converges in distribution to the Brownian bridge. The aim of this paper is to provide a new and simple proof of this fact.