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Nonparametric adaptive estimation for interacting particle systems

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  • Fabienne Comte
  • Valentine Genon‐Catalot

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.

Suggested Citation

  • Fabienne Comte & Valentine Genon‐Catalot, 2023. "Nonparametric adaptive estimation for interacting particle systems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(4), pages 1716-1755, December.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:4:p:1716-1755
    DOI: 10.1111/sjos.12661
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    References listed on IDEAS

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    1. Kay Giesecke & Gustavo Schwenkler & Justin A. Sirignano, 2020. "Inference for large financial systems," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 3-46, January.
    2. F. Comte & V. Genon-Catalot, 2020. "Regression function estimation on non compact support in an heteroscesdastic model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 93-128, January.
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