Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Estimation adaptative dans le modèle single-index par l'approche d'oracle (1304.6958v1)

Published 25 Apr 2013 in math.ST, math.PR, and stat.TH

Abstract: In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated possesses the single-index structure where neither the link function nor the index vector is known. We propose a novel procedure that adapts simultaneously to the unknown index and smoothness of link function. For the proposed procedure, we present a "local" oracle inequality (described by the pointwise seminorm), which is then used to obtain the upper bound on the maximal risk under regularity assumption on the link function. The lower bound on the minimax risk shows that the constructed estimator is optimally rate adaptive over the considered range of classes. For the same procedure we also establish a "global" oracle inequality (under the $ L_r $ norm, $r< \infty $) and study its performance over the Nikol'skii classes. This study shows that the proposed method can be applied to estimating functions of inhomogeneous smoothness.

Summary

We haven't generated a summary for this paper yet.