On rate-optimal nonparametric wavelet regression with long memory moving average errors |
| |
Authors: | Linyuan Li Kewei Lu |
| |
Institution: | 1. Department of Mathematics and Statistics, University of New Hampshire, Durham, NH, 03824, USA
|
| |
Abstract: | We consider the wavelet-based estimators of mean regression function with long memory moving average errors and investigate their asymptotic rates of convergence based on thresholding of empirical wavelet coefficients. We show that these estimators achieve nearly optimal minimax convergence rates within a logarithmic term over a large range of Besov function classes $B^{s}_{p,q}$ B p , q s . Therefore, in the presence of long memory non-Gaussian moving average noise, wavelet estimators still achieve nearly optimal convergence rates and provide explicitly the extraordinary local adaptability. The theory is illustrated with some numerical examples. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|