Some Functional Large Deviations Principles in Nonparametric Function Estimation

In this paper, we investigate functional large deviation behaviors of some nonparametric function estimates. As a first step, we define a a vector process Wn and study its large deviation behavior in the space L1×L1×L1 with respect to the weak convergence topology. As by-products, we derive large deviation principles in the L1-space equipped with the weak convergence topology simultaneously for several density and regression estimators built up using the delta-sequence estimation method.