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Last edited on
Oct 18, 2021 by JJ
.
Thesis:
Bachelor in Mathematics

Author:
Hannah Kümpel

Title:
A Bernstein von Mises theorem for nonparametric regression

Supervisor:
Jan JOHANNES

Abstract:
The Bernstein von Mises theorem establishes an important link between Bayesian and frequentist statistics by showing that both approaches will often yield an asymptotically equivalent result. After contrasting the Bayesian and frequentist approach as well as delineating the essential statement of the Bernstein von Mises theorem for parametric statistical models, this thesis aims to illustrate the process of first constructing a nonparametric statistical model in which a Bernstein von Mises result can be proven and eventually proving such a theorem. Based on the work of Castillo and Nickl (2014), said process will rely on Hilbert space techniques but also introduce multiscale spaces. While some resulting methods may be applied to several models, the focus will remain solely on the issue of nonparametric regression throughout.

References:
I. Castillo and R. Nickl. On the Bernstein–von Mises phenomenon for nonparametric Bayesprocedures. The Annals of Statistics 42(5):1941–1969, 2014.