In this paper, we investigate functional large deviation behaviors of some nonparametric function estimates. As a first step, we define a a vector process W n and study its large deviation behavior in the space L 1×L 1×L 1 with respect to the weak convergence topology. As by-products, we derive large deviation principles in the L 1-space equipped with the weak convergence topology simultaneously for several density and regression estimators built up using the delta-sequence estimation method.
