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Posterior inference in curved exponential families under increasing dimensions

Authors: Alexandre Belloni and Victor Chernozhukov
Date: 30 December 2013
Type: cemmap Working Paper, CWP68/13
DOI: 10.1920/wp.cem.2013.6813


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 moment restrictions, and plays a fundamental role in econometrics and other 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. In the process we also revisit and improve 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 multinomial 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.

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Now published:
Alexandre Belloni and Victor Chernozhukov June 2014, Posterior inference in curved exponential families under increasing dimensions, Journal article, Wiley

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