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Last edited on
Jun 20, 2025 by JJ.
Jan JOHANNES May 16,2025 Theses
Thesis:
Bachelor in Mathematics

Author:
Jonathan Richter

Title:
Asymptotics for Lasso-type estimators

Supervisor:
Jan JOHANNES

Abstract:
In this thesis we consider the class of Bridge estimators, which minimize the residual sum of squares plus an additional lq penalty term for q > 0. Prominent examples of this class are Lasso and Ridge regression, which are characterized by their l1 and l2 penalty terms, respectively. We establish the consistency of Bridge estimators under certain conditions and derive their asymptotic limiting distribution. We show that in some cases, these estimators have the inherent property of performing automatic variable selection, as their limiting distributions put positive probability mass on 0 when the true parameter is 0. Furthermore, we introduce a variety of algorithms to compute Bridge estimators.

References:
K. Knight and W. Fu. Asymptotics for Lasso-type estimators, The Annals of Statistics, 28(5):1356–1378, 2000.