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：本文考虑基于高频数据的潜变量扩散过程结构方程模型。针对该模型中的参数，提出拟似然估计量，并基于拟似然比推导拟合优度检验。同时处理结构方程模型中的稀疏估计问题，发展相应的拟合优度检验。进一步，对所提估计量的渐近性质进行系统研究。