论文标题
非同步观察的扩散过程渐近效率估计
Asymptotically efficient estimation for diffusion processes with nonsynchronous observations
论文作者
论文摘要
我们研究系数为非随机量并以非同步方式发生观察时，对扩散过程的最大样品类型估计。当我们考虑对金融市场中高频数据的分析时，非同步观察的问题很重要。构建一个准样品函数来定义估计量，我们可以自适应地估计扩散部分和漂移部分的参数。当终端时间点$ t_n $和观察频率变为无穷大时，我们会考虑渐近理论，并显示估计量的一致性和渐近正态性。此外，我们显示了统计模型的局部渐近正态性，因此估计值的渐近效率。为了显示最大样品类估计量的渐近性能，我们需要控制采样方案某些功能的渐近行为。尽管很难直接控制那些人，但我们研究了通过混合过程产生采样方案时可进行的足够条件。
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis of high-frequency data in a financial market. Constructing a quasi-likelihood function to define the estimator, we adaptively estimate the parameter for the diffusion part and the drift part. We consider the asymptotic theory when the terminal time point $T_n$ and the observation frequency goes to infinity, and show the consistency and the asymptotic normality of the estimator. Moreover, we show local asymptotic normality for the statistical model, and asymptotic efficiency of the estimator as a consequence. To show the asymptotic properties of the maximum-likelihood-type estimator, we need to control the asymptotic behaviors of some functionals of the sampling scheme. Though it is difficult to directly control those in general, we study tractable sufficient conditions when the sampling scheme is generated by mixing processes.
