Mean-field nonparametric estimation of interacting particle systems
Mean-field nonparametric estimation of interacting particle systems
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发表时间：
2022-05
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通讯作者：
Rentian Yao;Xiaohui Chen;Yun Yang
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作者：
Rentian Yao;Xiaohui Chen;Yun Yang
本文涉及相互作用的$ n $零件系统中分配状态依赖性漂移矢量场的非参数估计问题。观察每个粒子的单个标记数据，我们得出了最大似然估计量（MLE）的平均场收敛速率，这取决于函数类别的高斯复杂性和Rademacher复杂性。特别是，当函数类包含$ \ alpha $ -smooth h {\“ o} lder函数时，我们的收敛速率在$ n^{ - \ frac {\ alpha} {d+2+2+2 \ frac { - \ frac { - \ frac { - \ frac { - \ frac {d+2 \ alpha}} $与傅立叶分析卷积参数相结合，我们得出了MLE的一致性在McKean-Vlasov方程中。
This paper concerns the nonparametric estimation problem of the distribution-state dependent drift vector field in an interacting $N$-particle system. Observing single-trajectory data for each particle, we derive the mean-field rate of convergence for the maximum likelihood estimator (MLE), which depends on both Gaussian complexity and Rademacher complexity of the function class. In particular, when the function class contains $\alpha$-smooth H{\"o}lder functions, our rate of convergence is minimax optimal on the order of $N^{-\frac{\alpha}{d+2\alpha}}$. Combining with a Fourier analytical deconvolution argument, we derive the consistency of MLE for the external force and interaction kernel in the McKean-Vlasov equation.