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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
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