A Note on Block-Thresholded Wavelet Estimators with Correlated Noise

作者：Li Linyuan^*; Xiao Yimin

来源：Communications in Statistics - Theory and Methods, 2010, 39(7): 1111-1128.

DOI：10.1080/03610920902846570

• Block thresholding
• Long range dependence data
• Minimax estimation
• Nonlinear wavelet-based estimator
• Rates of convergence

Hall et al. (1999) proposed block-thresholding methods to estimate mean regression functions with independent random errors. They showed that block-thresholded wavelet estimators attain minimax-optimal convergence rates when the mean functions belong to a large class of functions that involve a wide variety of irregularities, including chirp and Doppler functions, and functions with jump discontinuities. In this article, we show that block-thresholded wavelet estimators still attain minimax convergence rates when the mean functions belong to a wide range of Besov classes [image omitted] (where s1/p, p epsilon 1 and q epsilon 1) with long-memory Gaussian errors. Therefore, in the presence of long-memory Gaussian errors, wavelet estimators still provide extensive adaptivity.

• 出版日期2010