Refining the central limit theorem approximation via extreme value theory

Ulrich K. Müller

Statistics & Probability Letters, 2019, vol. 155, issue C, -

Abstract: We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the sum of the smaller summands. If the tail is well approximated by a Pareto density, then this new approximation has substantially smaller error rates compared to the usual normal approximation for underlying distributions with finite variance and less than three moments. It can also provide an accurate approximation for some infinite variance distributions.

Keywords: Regular variation; Rates of convergence (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016771521930210X
Full text for ScienceDirect subscribers only

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:eee:stapro:v:155:y:2019:i:c:5

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2019.108564

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().