Sparse inference of structural equation modeling with latent variables for diffusion processes

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 inference in the SEM. The goodness-of-fit test for the sparse inference in the SEM is developed. Furthermore, the asymptotic properties of our proposed estimators and test statistics are examined.