How many distribution functions are there? Bracketing entropy bounds for high dimensional distribution functions
Shuguang Song (Boeing) Jon A. Wellner (University of Washington)
TL;DR
This paper investigates the complexity of high-dimensional distribution functions by establishing bracketing entropy bounds, aiming to understand their structural properties and limitations.
Contribution
The paper provides new theoretical bounds on the bracketing entropy of high-dimensional distribution functions, advancing the understanding of their complexity.
Findings
Derived upper bounds on bracketing entropy for high-dimensional distributions
Identified limitations and potential errors in previous bounds
Contributed to the theoretical framework of distribution function complexity
Abstract
This paper has been withdrawn by the authors due to a crucial error in a bound on page 19 and some other errors earlier in the paper.
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Taxonomy
TopicsNonlinear Partial Differential Equations