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Last edited on
Jun 20, 2025 by JJ.
Jan JOHANNES Nov 29,2024 Theses
Thesis:
Master in Mathematics

Author:
Alina Telge

Title:
Adaptive estimation in autoregression via model selection

Supervisors:
Jan JOHANNES

Abstract:
We study the problem of estimating an unknown regression function in a β-mixing dependent framework. For this, we consider least-squares estimators over a finite collection of finite dimensional spaces. By using the penalized least-squares estimator (PLSE) we can select an estimator from this collection of models. We state a non-asymptotic risk bound for this estimator and apply the estimation procedure for the case of an autoregressive model. Furthermore, we illustrate the PLSE in a simulation for different underlying regression functions.

Reference:
Y. Baraud, F. Comte, und G. Viennet. Adaptive Estimation in Autoregression or β-Mixing Regression via Model Selection, The Annals of Statistics 29:3,839–875, 2001.