Posterior Inference in Curved Exponential Families Under Increasing Dimensions

In this work we study 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, such as moment restrictions, on the model, and plays a fundamental role in various branches of data analysis. We establish conditions under which the posterior distribution is approximately normal, which in turn implies various good properties of estimation and inference procedures based on the posterior. We also discuss the multinomial model with moment restrictions, which arises in a variety of econometric applications. In our analysis, both the parameter dimension and the number of moments are increasing with the sample size