Article No. ectj?????? Econometrics Journal (2014), volume 10, pp. 1–26. Posterior Inference in Curved Exponential Families under Increasing Dimensions

Summary This work studies the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions on the model, such as mo-ment restrictions, and plays a fundamental role in econometrics and others branches of data analysis. We establish conditions under which the posterior distribution is ap-proximately normal, which in turn implies various good properties of estimation and inference procedures based on the posterior. In the process we also revisit and im-prove upon previous results for the exponential family under increasing dimension by making use of concentration of measure. We also discuss a variety of applications to high-dimensional versions of the classical econometric models including the multino-mial model with moment restrictions, seemingly unrelated regression equations, and single structural equation models. In our analysis, both the parameter dimension and the number of moments are increasing with the sample size