Remarks on Kneip's linear smoothers
S\"oren R. K\"unzel, David Pollard, Dana Yang
TL;DR
This paper revisits Kneip's 1994 analysis of ordered linear smoothers to clarify its implications and demonstrate how it supports the oracle inequality discussed by Tsybakov in 2014.
Contribution
It provides a reinterpretation of Kneip's results, connecting them explicitly to the oracle inequality framework in statistical learning theory.
Findings
Clarifies the connection between Kneip's smoothers and oracle inequalities
Reworks Kneip's analysis to demonstrate its implications
Bridges Kneip's work with Tsybakov's theoretical results
Abstract
We were trying to understand the analysis provided by Kneip (1994, Ordered Linear Smoothers). In particular we wanted to persuade ourselves that his results imply the oracle inequality stated by Tsybakov (2014, Lecture 8). This note contains our reworking of Kneip's ideas.
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Taxonomy
TopicsAdvanced Banach Space Theory · Optimization and Variational Analysis · Mathematical Inequalities and Applications