centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre


Keep in touch

Subscribe to cemmap news

Posterior inference in curved exponential families under increasing dimensions

Authors: Alexandre Belloni and Victor Chernozhukov
Date: 02 June 2014
Type: Journal article, Econometrics Journal, Vol. 17,No. 2, pp.S75–S100
DOI: 10.1111/ectj.12027


In this paper, we study the large-sample properties of the posterior-based inference in the curved exponential family under increasing dimensions. 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 others 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 dimensions by making use of concentration of measure. We also discuss a variety of applications to high-dimensional versions of 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 dimensions and the number of moments are increasing with the sample size.

Download full version
Previous version:
Alexandre Belloni and Victor Chernozhukov December 2013, Posterior inference in curved exponential families under increasing dimensions, cemmap Working Paper, Cemmap

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us