On the consistency of incomplete U-statistics under infinite second-order moments
Alexander Dürre and
Davy Paindaveine
Statistics & Probability Letters, 2023, vol. 193, issue C
Abstract:
We derive a consistency result, in the L1-sense, for incomplete U-statistics in the non-standard case where the kernel at hand has infinite second-order moments. Assuming that the kernel has finite moments of order p(≥1), we obtain a bound on the L1 distance between the incomplete U-statistic and its Dirac weak limit, which allows us to obtain, for any fixed p, an upper bound on the consistency rate. Our results hold for most classical sampling schemes that are used to obtain incomplete U-statistics.
Keywords: Consistency; Convergence rates; Incomplete U-statistics; Moment assumptions (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715222002279
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:193:y:2023:i:c:s0167715222002279
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.2022.109714
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 ().