The invariance principle for conditional empirical processes formed by dependent random variables
Денис Владимирович Порывай · Izvestiya Mathematics · 2005
We prove the convergence of finite-dimensional distributions and establish density for Nadaraya-Watson conditional empirical processes. The observations are assumed to be described by a strictly stationary sequence of random variables whose mixing coefficients decay polynomially. The proof of density of such processes in the space of continuous functionals uses entropy conditions on the class of indexing functions.