Asymptotic normality of the recursive kernel regression estimate under dependence conditions.(English)Zbl 0925.62171

Let $$\{(X_i,Y_i)\}_{i\geq 1}$$ be a strictly stationary and $$\alpha$$-mixing stochastic process, where $$X_i$$ and $$Y_i$$ are $$d$$- and one-dimensional random variables, resp. The authors study the limit behavior of certain recursive kernel estimators of the conditional expectation $$m(x) = E(Y_1| X_1=x), x\in R^d$$.

MSC:

 62G20 Asymptotic properties of nonparametric inference 62G07 Density estimation
Full Text: