Central limit theorems for vector-valued composite functionals with smoothing and applications

Huihui Chen (), Darinka Dentcheva (), Yang Lin () and Gregory J. Stock ()
Additional contact information
Huihui Chen: Stevens Institute of Technology
Darinka Dentcheva: Stevens Institute of Technology
Yang Lin: Hartford Steam Boiler
Gregory J. Stock: Raritan Valley Community College

Annals of the Institute of Statistical Mathematics, 2025, vol. 77, issue 5, No 8, 852 pages

Abstract: Abstract This paper focuses on vector-valued composite functionals, which may be nonlinear in probability. Our goal is establishing central limit theorems for these functionals when employed by mixed estimators. Our study is relevant to the evaluation and comparison of risk in decision-making contexts and extends to functionals that arise in machine learning. A generalized family of composite risk functionals is presented, which encompasses coherent risk measures, including systemic risk. The paper makes two main contributions. First, we analyze vector-valued functionals and provide a framework for evaluating high-dimensional risks. This enables comparison of multiple risk measures and supports estimation and asymptotic analysis of systemic risk and its optimal value in decision-making. Second, we derive new central limit theorems for optimized composite functionals using mixed estimators, including empirical and smoothed types. We give verifiable conditions for central limit formulae and demonstrate their applicability to several risk measures.

Keywords: Coherent measure of risk; Stochastic programming; Systemic risk (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10463-025-00934-z 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:aistmt:v:77:y:2025:i:5:d:10.1007_s10463-025-00934-z

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-025-00934-z

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().