Convergence of the Reduced Empirical Process for Non-I.I.D. Random Vectors

The Annals of Statistics · 1975 · Volume 3 · Issue 2

Abstract

Any triangular array of row independent random vectors with continuous df's has a standard reduction to random vectors with values in the unit cube. The reduced empirical process belonging to the transformed random vectors is always relatively compact. Weak convergence to a (necessarily Gaussian) process holds iff the corresponding covariance kernel converges pointwise.

Keywords

60B10, 60G15, convergence of the empirical process, Non. i.i.d. random-vectors

Enable JavaScript for citation tools and additional paper interactions.