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We consider the residual empirical process in random design regression with long memory errors. We establish its limiting behaviour, showing that its rates of convergence are different from the rates ...
This paper describes limiting behaviour of tail empirical process associated with long memory stochastic volatility models. We show that such process has dichoto- mous behaviour, according to an int...
A new approximation of the unifonn empirical and quantile processes results in a weak invariance principle indexed by functions for the general empirical process. Consequences of this result are we...
Let E,, be a uniform empirical process and A (respectively, v3 the unique location of its maximum (respectively, midimum). We establish a "liminP' iterated logarithm law for (a-v).
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...
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.
In this paper we study the asymptotic behaviour of empirical processes when parameters are estimated, assuming that the underlying sequence of random variables is long-range dependent. We show compl...

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