  Latent space models are powerful statistical tools for modeling and
understanding network data. While the importance of accounting for uncertainty
in network analysis has been well recognized, the current literature
predominantly focuses on point estimation and prediction, leaving the
statistical inference of latent space models an open question. This work aims
to fill this gap by providing a general framework to analyze the theoretical
properties of the maximum likelihood estimators. In particular, we establish
the uniform consistency and asymptotic distribution results for the latent
space models under different edge types and link functions. Furthermore, the
proposed framework enables us to generalize our results to the dependent-edge
and sparse scenarios. Our theories are supported by simulation studies and have
the potential to be applied in downstream inferences, such as link prediction
and network testing problems.
