Asymptotic distribution of smoothers based on local means and local medians under dependence (Q1898396)

Let \(\{(X_t,Y_t)\), \(t\geq p+1\}\) be a strictly stationary process, \(X_t\in \mathbb{R}^p\), \(Y_t\in \mathbb{R}\), with the same distribution function as the vector \((X,Y)\). We will study the asymptotic distribution of some nonparametric estimators of the conditional expectation \(r(x)= E(Y\mid X=x)\). As is well known, if we allow dependence on the observed sample, this framework includes usual nonparametric regression with dependent errors. Also, autoregressive models can be considered by taking \(X_t= (Y_{t-1},\dots, Y_{t-p})\).