离散观测扩散过程因子分析中的统计推断
Statistical inference in factor analysis for diffusion processes from discrete observations
摘要：
我们考虑离散观测的遍历和非遍历扩散过程的因子分析中的统计推断。在高维协方差阵估计领域，主要讨论了基于高频时间序列数据的因子模型。在这一领域，主要采用基于主成分分析的方法。然而，该方法仅对高维模型有效。另一方面，有一种基于拟似然的方法。然而，由于假设该因素是可观察的，因此当该因素是潜在的时，我们不能使用该方法。因此，现有的方法是不有效的，当因素是潜在的，可观察变量的维数不是很高。因此，我们提出了一种有效的方法，在这种情况下。
英文摘要：
We consider statistical inference in factor analysis for ergodic and non-ergodic diffusion processes from discrete observations. Factor model based on high frequency time series data has been mainly discussed in the field of high dimensional covariance matrix estimation. In this field, the method based on principal component analysis has been mainly used. However, this method is effective only for high dimensional model. On the other hand, there is a method based on the quasi-likelihood. However, since the factor is assumed to be observable, we cannot use this method when the factor is latent. Thus, the existing methods are not effective when the factor is latent and the dimension of the observable variable is not so high. Therefore, we propose an effective method in the situation.
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