1992/03/01 by Young K. Truong, Charles J. Stone · 2 citations
Engineering · Computer Science · Mathematics · #Control Systems and Identification #Time Series Analysis and Forecasting #Fuzzy Systems and Optimization
paper · pdf · doi:10.1214/aos/1176348513
openalex publication_date 1992/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
Consider a stationary time series (Xt, Yt), t = 0, ± 1,…, with Xt being ℝd-valued and Yt real-valued. The conditional mean function is given by θ(X0) = E(Y0\midX0). Under appropriate regularity conditions, a local average estimator of this function based on a finite realization (X1, Y1),…,(Xn, Yn) can be chosen to achieve the optimal rate of convergence n-1/(2 + d) both pointwise and in L2 norms restricted to a compact; and 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. Similar results hold for local median estimators of the conditional median function, which is given by θ(X0) = med(Y0\midX0).