Alexandre Belloni, Victor Chernozhukov
arXiv 20 Apr 2009 · Mathematics — Statistics Theory · publishedEconometrics Journal (2014) · 3 citations (OpenAlex)
arXiv:0904.3132 · PDF · DOI · OpenAlex · Extracted main text
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 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 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.
appendix boundary found by appendix_titled_section at “Appendix A: Technical Results” · 40% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Ghosal, S (2000) Asymptotic normality of posterior distributions for exponential families when the number of parameters tends to infinity | 0.937 | 17 | 5 | 82% |
| 2 | Zellner, A (1962) An efficient method of estimating seemingly unrelated regressions and tests of aggregation bias | 0.737 | 4 | 3 | 50% |
| 3 | Portnoy, S (1988) Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity | 0.693 | 6 | 4 | 33% |
| 4 | van Garderen, K. J (1997) Curved Exponential Models in Econometrics | 0.644 | 3 | 2 | 67% |
| 5 | Chamberlain, G (1987) Asymptotic efficiency in estimation with conditional moment restrictions | 0.644 | 2 | 2 | 100% |
| 6 | Imbens, G. W (1997) One-step estimators for over-identified generalized method of moments models | 0.644 | 2 | 2 | 100% |
| 7 | Zellner, A (1971) An Introduction to Bayesian Inference in Econometrics | 0.644 | 2 | 2 | 100% |
| 8 | Efron, B (1978) The Geometry of Exponential Families | 0.511 | 2 | 1 | 100% |
| 9 | Belloni, A. and V. Chernozhukov (2009) On the Computational Complexity of MCMC-based Estimators in Large Samples self | 0.405 | 1 | 1 | 100% |
| 10 | Bontemps, D (2011) Bernstein-von Mises theorems for Gaussian regression with increasing number of regressors | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 46 scored citations.