## The Annals of Statistics

### Nonparametric Function Estimation for Time Series by Local Average Estimators

Lanh Tat Tran

#### 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

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