We consider structural equation modeling (SEM) with latent variables for diffusion processes based on high-frequency data. The quasi-likelihood estimators for parameters in the SEM are proposed. The goodness-of-fit test is derived from the quasi-likelihood ratio. We also treat sparse estimation in the SEM. The goodness-of-fit test for the sparse estimation in the SEM is developed. Furthermore, the asymptotic properties of our proposed estimators are examined.

翻译：考虑基于高频数据的含潜变量扩散过程的结构方程建模。提出该结构方程模型中参数的拟似然估计量,基于拟似然比导出拟合优度检验。同时处理结构方程模型中的稀疏估计问题,发展出针对稀疏估计的拟合优度检验。进一步考察了所提估计量的渐近性质。