We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed – random vectors, combining mean and extreme behaviors. It extends the so-called ’normex’ – approach from a univariate to a multivariate framework. We propose two possible multinormex – distributions, named d-Normex and MRV-Normex. Both rely on the Gaussian distribution – for describing the mean behavior, via the CLT, while the difference between the – two versions comes from using the exact distribution or the EV theorem for the maximum. – The main theorems provide the rate of convergence for each version of the multi-normex – distributions towards the distribution of the sum, assuming second order regular variation – property for the norm of the parent random vector when considering the MRV-normex – case. Numerical illustrations and comparisons are proposed with various dependence structures – on the parent random vector, using QQ-plots based on geometrical quantiles.
KRATZ, M. et PROKOPENKO, E. (2021). Multi-Normex Distributions for the Sum of Random Vectors. Rates of Convergence. 2102, ESSEC Business School.