Posterior inference in curved exponential families under increasing dimensions
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 econom...
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| Format: | Article |
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Wiley-Blackwell
2018
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| Online Access: | http://hdl.handle.net/1721.1/114403 https://orcid.org/0000-0002-3250-6714 |
| _version_ | 1826194360644927488 |
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| author | Belloni, Alexandre Chernozhukov, Victor V |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Belloni, Alexandre Chernozhukov, Victor V |
| author_sort | Belloni, Alexandre |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:54:48Z |
| format | Article |
| id | mit-1721.1/114403 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:54:48Z |
| publishDate | 2018 |
| publisher | Wiley-Blackwell |
| record_format | dspace |
| spelling | mit-1721.1/1144032024-06-28T14:01:52Z Posterior inference in curved exponential families under increasing dimensions Belloni, Alexandre Chernozhukov, Victor V Massachusetts Institute of Technology. Department of Economics Chernozhukov, Victor V 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. National Science Foundation (U.S.) Sloan Foundation (Research Fellowship) 2018-03-27T17:16:52Z 2018-03-27T17:16:52Z 2014-02 2012-01 2018-02-20T18:41:14Z Article http://purl.org/eprint/type/JournalArticle 1368-4221 1368-423X http://hdl.handle.net/1721.1/114403 Belloni, Alexandre, and Victor Chernozhukov. “Posterior Inference in Curved Exponential Families under Increasing Dimensions: Posterior Inference in Curved Exponential.” The Econometrics Journal, vol. 17, no. 2, June 2014, pp. S75–100. https://orcid.org/0000-0002-3250-6714 http://dx.doi.org/10.1111/ECTJ.12027 The Econometrics Journal Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Wiley-Blackwell arXiv |
| spellingShingle | Belloni, Alexandre Chernozhukov, Victor V Posterior inference in curved exponential families under increasing dimensions |
| title | Posterior inference in curved exponential families under increasing dimensions |
| title_full | Posterior inference in curved exponential families under increasing dimensions |
| title_fullStr | Posterior inference in curved exponential families under increasing dimensions |
| title_full_unstemmed | Posterior inference in curved exponential families under increasing dimensions |
| title_short | Posterior inference in curved exponential families under increasing dimensions |
| title_sort | posterior inference in curved exponential families under increasing dimensions |
| url | http://hdl.handle.net/1721.1/114403 https://orcid.org/0000-0002-3250-6714 |
| work_keys_str_mv | AT bellonialexandre posteriorinferenceincurvedexponentialfamiliesunderincreasingdimensions AT chernozhukovvictorv posteriorinferenceincurvedexponentialfamiliesunderincreasingdimensions |