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Title: Nadaraya–Watson kernel smoothing as a random energy model
Abstract Precise asymptotics have revealed many surprises in high-dimensional regression. These advances, however, have not extended to perhaps the simplest estimator: direct Nadaraya–Watson (NW) kernel smoothing. Here, we describe how one can use ideas from the analysis of the random energy model (REM) in statistical physics to compute sharp asymptotics for the NW estimator when the sample size is exponential in the dimension. As a simple starting point for investigation, we focus on the case in which one aims to estimate a single-index target function using a radial basis function kernel on the sphere. Our main result is a pointwise asymptotic for the NW predictor, showing that it re-scales the argument of the true link function. Our work provides a first step towards a detailed understanding of kernel smoothing in high dimensions.  more » « less
Award ID(s):
2239780 2134157
PAR ID:
10650506
Author(s) / Creator(s):
;
Publisher / Repository:
IOP Publishing Ltd
Date Published:
Journal Name:
Journal of Statistical Mechanics: Theory and Experiment
Volume:
2025
Issue:
1
ISSN:
1742-5468
Page Range / eLocation ID:
013404
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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