论文标题
McKean-Vlasov模型的LAN属性在平均场状态下
The LAN property for McKean-Vlasov models in a mean-field regime
论文作者
论文摘要
我们建立了局部渐近正态性（LAN）属性，用于估计$ n $相互作用粒子系统在固定时间范围内观察到的多维参数，该系统在固定时间范围内观察到了平均场式$ n \ rightarrow \ rightarrow \ infty $。通过实施Ibragimov和Hasminski的经典理论，我们特别获得了最大似然估计器的敏锐结果，这要归功于Hájek的卷积定理和对可能性过程产生渐近最小值最小值的可能性过程的强大控制，这超出了其简单的渐近正态性。我们的结构结果为随附的非线性McKean-Vlasov实验带来了一些光线，并使我们能够得出简单明了的标准，以获得Fisher信息矩阵的可识别性和非降低性。这些条件对于其他有关相互作用扩散参数推断的主题的研究也引起了人们的关注。
We establish the local asymptotic normality (LAN) property for estimating a multidimensional parameter in the drift of a system of $N$ interacting particles observed over a fixed time horizon in a mean-field regime $N \rightarrow \infty$. By implementing the classical theory of Ibragimov and Hasminski, we obtain in particular sharp results for the maximum likelihood estimator that go beyond its simple asymptotic normality thanks to Hájek's convolution theorem and strong controls of the likelihood process that yield asymptotic minimax optimality (up to constants). Our structural results shed some light to the accompanying nonlinear McKean-Vlasov experiment, and enable us to derive simple and explicit criteria to obtain identifiability and non-degeneracy of the Fisher information matrix. These conditions are also of interest for other recent studies on the topic of parametric inference for interacting diffusions.
