ROBUST NONPARAMETRIC REGRESSION IN TIME-SERIES

Consider a stationary time series (Xt, Yt), t = 0, ±1, ... with Xt being Rd-valued and Yt real-valued. Let ψ(·) denote a monotone function and let θ(·) denote the robust conditional location functional so that E[ψ(Y0 - θ(X0))|X0] = 0. Given a finite realization (X1, Y1), ..., (Xn, Yn), the problem of estimating θ(·) is considered. Under appropriate regularity conditions, it is shown that a sequence of the robust conditional location functional estimators can be chosen to achieve the optimal rate of convergence n -1 (2 + d) both pointwise and in Lq (1 ≤ q < ∞) norms restricted to a compact; it can also be chosen to achieve the optimal rate of convergence (n-1 log(n)) 1 (2 + d) in L∞ norm restricted to a compact. © 1992.