Multi-normex distributions for the sum of random vectors. Rates of convergence Full article
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Extremes
ISSN: 1386-1999 |
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| Output data | Year: 2023, Volume: 26, Number: 3, Pages: 509–544 Pages count : 36 DOI: 10.1007/s10687-022-00461-7 | ||||
| Tags | Aggregation · Central limit theorem · Dependence · Extreme value theorem · Geometrical quantiles · Multivariate extremes · Multivariate regular variation · (Multivariate) Pareto distribution · Ordered statistics · QQ-plots · Rate of convergence · Second order regular variation · Sum of random vectors | ||||
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Abstract:
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 multi-normex 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.
Cite:
Kratz M.
, Prokopenko E.
Multi-normex distributions for the sum of random vectors. Rates of convergence
Extremes. 2023. V.26. N3. P.509–544. DOI: 10.1007/s10687-022-00461-7 WOS Scopus РИНЦ OpenAlex
Multi-normex distributions for the sum of random vectors. Rates of convergence
Extremes. 2023. V.26. N3. P.509–544. DOI: 10.1007/s10687-022-00461-7 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Oct 20, 2021 |
| Accepted: | Dec 21, 2022 |
| Published online: | Jan 13, 2023 |
| Published print: | Sep 14, 2023 |
Identifiers:
| Web of science: | WOS:000935590100001 |
| Scopus: | 2-s2.0-85146222673 |
| Elibrary: | 60310309 |
| OpenAlex: | W4287071142 |