The Annals of Statistics

Nonparametric Function Estimation for Time Series by Local Average Estimators

Lanh Tat Tran

Full-text: Open access

Abstract

Let $(\mathbf{X}_t, Y_t)$ be a stationary time series with $\mathbf{X}_t$ being $R^d$-valued and $Y_t$ real valued, and where $Y_t$ is not necessarily bounded. Let $E(Y_0 \mid \mathbf{X}_0)$ be the conditional mean function. Under appropriate regularity conditions, local average estimators of this function can be chosen to achieve the optimal rate of convergence $(n^{-1} \log n)^{1/(d + 2)}$ in $L_\infty$ norm restricted to a compact. The result answers a question raised by Truong and Stone.

Article information

Source
Ann. Statist., Volume 21, Number 2 (1993), 1040-1057.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349163

Digital Object Identifier
doi:10.1214/aos/1176349163

Mathematical Reviews number (MathSciNet)
MR1232531

Zentralblatt MATH identifier
0790.62037

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62G05: Estimation 62G20: Asymptotic properties

Keywords
Nonparametric estimation strong mixing local mean

Citation

Tran, Lanh Tat. Nonparametric Function Estimation for Time Series by Local Average Estimators. Ann. Statist. 21 (1993), no. 2, 1040--1057. doi:10.1214/aos/1176349163. https://projecteuclid.org/euclid.aos/1176349163


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