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June, 1993 Nonparametric Function Estimation for Time Series by Local Average Estimators
Lanh Tat Tran
Ann. Statist. 21(2): 1040-1057 (June, 1993). DOI: 10.1214/aos/1176349163

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.

Citation

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Lanh Tat Tran. "Nonparametric Function Estimation for Time Series by Local Average Estimators." Ann. Statist. 21 (2) 1040 - 1057, June, 1993. https://doi.org/10.1214/aos/1176349163

Information

Published: June, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0790.62037
MathSciNet: MR1232531
Digital Object Identifier: 10.1214/aos/1176349163

Subjects:
Primary: 62G07
Secondary: 62G05, 62G20

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 2 • June, 1993
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