Nonparametric adaptive estimation for interacting particle systems

Fabienne Comte and Valentine Genon‐Catalot

Scandinavian Journal of Statistics, 2023, vol. 50, issue 4, 1716-1755

Abstract: We consider a stochastic system of N$$ N $$ interacting particles with constant diffusion coefficient and drift linear in space, time‐depending on two unknown deterministic functions. Our concern here is the nonparametric estimation of these functions from a continuous observation of the process on [0,T]$$ \left[0,T\right] $$ for fixed T$$ T $$ and large N$$ N $$. We define two collections of projection estimators belonging to finite‐dimensional subspaces of 𝕃2([0,T]). We study the 𝕃2‐risks of these estimators, where the risk is defined either by the expectation of an empirical norm or by the expectation of a deterministic norm. Afterwards, we propose a data‐driven choice of the dimensions and study the risk of the adaptive estimators. The results are illustrated by numerical experiments on simulated data.

Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/sjos.12661

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:bla:scjsta:v:50:y:2023:i:4:p:1716-1755

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().