Asymptotics in Multivariate Le Cam’s Theorem

V. Čekanavičius () and S. Jokubauskienė ()
Additional contact information
V. Čekanavičius: Vilnius University
S. Jokubauskienė: Vytautas Magnus University

Journal of Theoretical Probability, 2025, vol. 38, issue 4, 1-15

Abstract: Abstract The Multivariate version of Le Cam’s theorem states that any sum of shifted independent identically distributed random vectors can be approximated by an accompanying compound Poisson law with accuracy of the order $$O(n^{-1/3})$$ O ( n - 1 / 3 ) . We show that a suitably chosen asymptotic expansion can improve the accuracy of approximation. Results of this paper are closely related to the first uniform Kolmogorov theorem.

Keywords: Compound Poisson approximation; Convolution of distributions; Kolmogorov metric; Sums of random vectors; The first uniform Kolmogorov theorem; Primary 60F99; Secondary 60G50 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-025-01435-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:38:y:2025:i:4:d:10.1007_s10959-025-01435-8

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-025-01435-8

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().