High-Dimensional Central Limit Theorems for Homogeneous Sums

  title={High-Dimensional Central Limit Theorems for Homogeneous Sums},
  author={Yuta Koike},
  journal={Journal of Theoretical Probability},
  • Yuta Koike
  • Published 11 February 2019
  • Mathematics
  • Journal of Theoretical Probability
This paper develops a quantitative version of de Jong’s central limit theorem for homogeneous sums in a high-dimensional setting. More precisely, under appropriate moment assumptions, we establish an upper bound for the Kolmogorov distance between a multi-dimensional vector of homogeneous sums and a Gaussian vector so that the bound depends polynomially on the logarithm of the dimension and is governed by the fourth cumulants and the maximal influences of the components. As a corollary, we… 


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