Exponential bounds of mean error for the kernel estimates of regression functions

Let (X, Y), (X₁, Y₁), …, (X_n, Y_n) be i.d.d. R^r × R-valued random vectors with E|Y| < ∞, and let Q_n(x) be a kernel estimate of the regression function Q(x) = E(Y|X = x). In this paper, we establish an exponential bound of the mean deviation between Q_n(x) and Q(x) given the training sample Zⁿ = (X₁, Y₁, …, X_n, Y_n), under conditions as weak as possible.