论文标题
相互作用粒子系统的平均场非参数估计
Mean-Field Nonparametric Estimation of Interacting Particle Systems
论文作者
论文摘要
本文涉及相互作用的$ n $零件系统中分配状态依赖性漂移矢量场的非参数估计问题。观察每个粒子的单个标记数据，我们得出了最大似然估计量（MLE）的平均场收敛速率，这取决于函数类别的高斯复杂性和Rademacher复杂性。特别是，当函数类包含$α$ -Smooth H {Ö} lder函数时，我们的收敛速率在$ n^{ - \fracα{d+2α}} $的顺序上是最小的。结合一个傅立叶分析反卷积参数，我们得出了MCKEAN-VLASOV方程中外力和相互作用内核MLE的一致性。
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 $α$-smooth H{ö}lder functions, our rate of convergence is minimax optimal on the order of $N^{-\fracα{d+2α}}$. 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.
