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Last edited on
Oct 17, 2024 by JJ.
Jan JOHANNES May 17,2019 Theses
Thesis:
Bachelor in Mathematics

Author:
Alexander Sauer

Title:
Nonparametric regression on non compact sets

Supervisors:
Sergio Brenner Miguel and Jan JOHANNES

Abstract:
This thesis describes in great detail the paper Regression function estimation as a partly inverse problem by Fabienne Comte and Valentine Genon-Catalot from 2019. After introducing the projection estimator for nonparametric regression, we describe the model selection criterion proposed by the authors and explain their proof of optimality. Next, we discuss the differences between the compact and non compact case. Additionally, we illuminate the proof of an upper and lower bound for the rates of convergence of the estimator after presenting a general framework to prove such lower bounds following Tsybakov (2009). Finally, we provide some numerical illustrations.

References:
Comte and Genon-Catalot. Regression function estimation on a non compact support as a partly inverse problem., Technical report, hal-01690856 and Prépublication MAP5 2018-01.