In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the framework of [5] we develop a new randomized multilevel Monte Carlo method for estimating the parameters, based upon Markovian stochastic approximation methodology. New Markov chain Monte Carlo algorithms for the POMV model are introduced facilitating the application of [5]. We prove, under assumptions, that the expectation of our estimator is biased, but with expected small and controllable bias. Our approach is implemented on several examples.

翻译：本文针对一类具有离散时间观测的部分观测McKean-Vlasov（POMV）扩散过程，研究其在固定时间区间内静态参数的基于似然函数的估计方法。特别地，基于[5]的理论框架，我们结合马尔可夫随机逼近方法，提出了一种新的随机化多层蒙特卡洛参数估计算法。针对POMV模型，我们引入了新的马尔可夫链蒙特卡洛算法，从而实现了[5]中方法的有效应用。在满足假设条件的情况下，我们证明了该估计量的期望存在偏差，但该偏差具有期望值小且可控的特性。我们在多个示例上对所提方法进行了实现验证。