Exponential bounds of mean error for the kernel estimate of regression functions (Q1117632)

Let (X,Y), \((X_ 1,Y_ 1),...,(X_ n,Y_ n)\) be i.d.d. \(R^ r\times R\)-valued random vectors with \(E| Y| <\infty\), and let \(Q_ n(x)\) be a kernel estimate of the regression function \(Q(x)=E(Y|\) \(X=x)\). We establish an exponential bound of the mean deviation between \(Q_ n(x)\) and Q(x) given the training sample \(Z^ n=(X_ 1,Y_ 1,...,X_ n,Y_ n)\), under conditions as weak as possible.