2018/02/28 by Martin Raič · 1 citation
Mathematics · #Central limit theorem #Class (philosophy) #Constant (computer programming) #Geometry and complex manifolds #Independent and identically distributed random variables #Limit (mathematics) #Markov Chains and Monte Carlo Methods #Multivariate statistics #Random Matrices and Applications #Regular polygon #Upper and lower bounds #math.PR #msc:60F05
paper · pdf · doi:10.3150/18-bej1072
30 pages, 1 figure, 1 table
openalex created_date 2018/03/06 · arxiv created 2019/07/23 · arxiv updated 2019/07/24 · openalex publication_date 2019/09/13 · openalex updated_date 2026/08/05
We provide a Lyapunov type bound in the multivariate central limit theorem for sums of independent, but not necessarily identically distributed random vectors. The error in the normal approximation is estimated for certain classes of sets, which include the class of measurable convex sets. The error bound is stated with explicit constants. The result is proved by means of Stein's method. In addition, we improve the constant in the bound of the Gaussian perimeter of convex sets.