On Logarithmic Penalty in Adaptive Pointwise Estimation and Blockwise Wavelet Shrinkage

Abstract

A logarithmic penalty in adaptive pointwise estimation of a nonparametric regression function is one of the most intriguing and, at the same time, poorly understood statistical phenomena. This article uses computational, visualization, and theoretical methods to shed new light on where and how the penalty strikes in popular wavelet estimates.

Key Words:

• Nonparametric
• Oracle
• Regression
• Small sample
• Stein shrinkage
• Visualization