Imputation estimators for unnormalized models with missing data
This addresses a specific statistical inference problem for researchers dealing with missing data in complex models, but it appears incremental as it combines existing techniques rather than introducing a fundamentally new approach.
The paper tackles the problem of estimating statistical models with unnormalized densities when data is missing, by combining imputation techniques with existing estimators like noise contrastive estimation and score matching. The result is that the proposed methods enable effective statistical inference, as demonstrated in simulations with truncated Gaussian graphical models and real wind direction data.
Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to combine imputation techniques with estimators for unnormalized models including noise contrastive estimation and score matching. In addition, we derive asymptotic distributions of the proposed estimators and construct confidence intervals. Simulation results with truncated Gaussian graphical models and the application to real data of wind direction reveal that the proposed methods effectively enable statistical inference with unnormalized models from missing data.