LAN property for the parameter of the jump rate in mean field interacting systems of neurons
Abstract
In the context of a large system of N neurons interacting through spike events in a mean-field regime as N→ ∞, we characterize the estimation of a multidimensional parameter in the spiking rate, when the neural states are observed over a fixed time horizon. We first prove the local asymptotic normality (LAN) property and leverage classical theory to establish the asymptotic efficiency of the maximum likelihood estimator. While the theory of Ibragimov and Hasminskii yields strong results, up to global asymptotic minimax bound, its applicability appears currently limited to models without state resets at spike times. Following then Höpfner's classical approach, we nevertheless derive, in a general setting including neuron reset, the consistency, asymptotic normality and local asymptotic minimax optimality of the estimator.
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BibTeX
@misc{duarte2026property,
title = {{LAN property for the parameter of the jump rate in mean field interacting systems of neurons}},
author = {Aline Duarte and Dasha Loukianova and Aurélien Velleret},
howpublished = {HAL},
year = {2026},
month = jul,
eprint = {2605.03698},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05738658v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - LAN property for the parameter of the jump rate in mean field interacting systems of neurons
AU - Aline Duarte
AU - Dasha Loukianova
AU - Aurélien Velleret
PY - 2026
DA - 2026/07/31
PB - HAL
UR - https://hal.science/hal-05738658v1
AB - In the context of a large system of N neurons interacting through spike events in a mean-field regime as N→ ∞, we characterize the estimation of a multidimensional parameter in the spiking rate, when the neural states are observed over a fixed time horizon. We first prove the local asymptotic normality (LAN) property and leverage classical theory to establish the asymptotic efficiency of the maximum likelihood estimator. While the theory of Ibragimov and Hasminskii yields strong results, up to global asymptotic minimax bound, its applicability appears currently limited to models without state resets at spike times. Following then Höpfner's classical approach, we nevertheless derive, in a general setting including neuron reset, the consistency, asymptotic normality and local asymptotic minimax optimality of the estimator.
ER -