A data-driven block thresholding approach to wavelet estimation

TL;DR

This paper introduces a data-driven block thresholding method for wavelet regression that adaptively selects parameters to achieve near-minimax risk, demonstrating superior performance over existing estimators.

Contribution

It proposes a novel adaptive block thresholding procedure that optimally chooses block size and thresholds using Stein's risk estimate, improving wavelet estimation accuracy.

Findings

Achieves near-minimax risk over a wide class of Besov spaces.

Demonstrates superior finite sample performance in simulations.

Easily implementable with practical advantages.

Abstract

A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by minimizing Stein's unbiased risk estimate. The estimator is sharp adaptive over a class of Besov bodies and achieves simultaneously within a small constant factor of the minimax risk over a wide collection of Besov Bodies including both the ``dense'' and ``sparse'' cases. The procedure is easy to implement. Numerical results show that it has superior finite sample performance in comparison to the other leading wavelet thresholding estimators.