Project Details
Projekt
Computationally tractable bootstrap for high-dimensional data
Subject Area
Mathematics
Term
since 2021
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 460867398
In the big data era, running bootstrap procedures for high-dimensional massive data is computationally demanding. At the same time, statistics under high-dimensional scaling frequently exhibit some phase transition in terms of their underlying distribution and the imposed scaling. The situation is even more intricate in the presence of (unknown) dependency structures within the data. This interplay poses significant challenges for reliable bootstrap approximations. Combining subsampling of observations with suitable selection of their coordinates, a fully nonparametric and computationally tractable bootstrap algorithm especially for high-dimensional sample covariance matrices has been developed in the first funding period. In the next funding period, the difficulty of adapting to statistics’ phase transition phenomena is addressed and the new bootstrap methodology is pushed forward beyond independence. Additionally, the prior results are extended to more general matrices, especially to sample (auto)correlation matrices under minimal moment requirements. In this way, this project adds comprehensive simulationbased inference methodology to the Research Unit.
DFG Programme
Research Units
