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

Author:
Maria Frech

Title:
Minimax optimality of adaptive Fisher tests

Supervisors:
Sandra Schluttenhofer and Jan JOHANNES

Abstract:
In this thesis we consider an adaptive test, based on model selection, which is designed to test whether the expectation of a Gaussian vector with n independent components belongs to a linear subspace of the n-dimensional real numbers or to a nonparametric alternative. We choose the minimax approach to evaluate its performance. Further we discuss a general method for obtaining lower bounds on the minimax radius.

References:
Y. Baraud, S. Huet and B. Laurent. Adaptive tests of linear hypotheses by model selection. The Annals of Statistics, 31(1):225-251, 2003.