In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially observed diffusion process and work with the model with bias and consider maximizing the resulting log-likelihood. Using a novel double randomization scheme, based upon Markovian stochastic approximation we develop a new method to unbiasedly estimate the static parameters, that is, to obtain the maximum likelihood estimator with no time discretization bias. Under assumptions we prove that our estimator is unbiased and investigate the method in several numerical examples, showing that it can empirically out-perform existing unbiased methodology.

翻译：本文考虑在固定时间区间内，基于离散时间观测对部分观测扩散过程的静态参数进行估计。具体而言，我们假设必须对部分观测扩散过程进行时间离散化，并在带偏差的模型框架下开展工作，同时考虑最大化由此产生的对数似然函数。通过采用一种基于马尔可夫随机逼近的新型双重随机化方案，我们开发了一种新方法来无偏估计静态参数，即获取无时间离散化偏差的最大似然估计量。在给定假设条件下，我们证明了所提估计量的无偏性，并通过多个数值算例对该方法进行了验证，结果表明其在经验性能上优于现有无偏方法。