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math.ST2026
Optimal neural network approximation of smooth compositional functions on sets with low intrinsic dimension
Thomas Nagler, Sophie Langer
We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal un…
math.ST2025
Properties of stepwise parameter estimation in high-dimensional vine copulas
Jana Gauss, Thomas Nagler
The increasing use of vine copulas in high-dimensional settings, where the number of parameters is often of the same order as the sample size, calls for asymptotic theory beyond th…
math.ST2024
Asymptotics for estimating a diverging number of parameters -- with and without sparsity
Jana Gauss, Thomas Nagler
We develop a general asymptotic theory for estimating equations whose dimension diverges with the sample size. For both unpenalized and sparse penalized problems, we establish popu…