Siddhartha Chib, Minchul Shin, Anna Simoni
arXiv 26 Oct 2021 · Mathematics — Statistics Theory · publishedJournal of the Royal Statistical Society Series B (Statistical Methodology) (2021) · 4 citations (OpenAlex)
arXiv:2110.13531 · PDF · DOI · OpenAlex · Extracted main text
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed to satisfy a sequence of unconditional moments based on an increasing (in sample size) vector of approximating functions (such as tensor splines based on the splines of each conditioning variable). For any given sample size, results are robust to the number of expanded moments. We derive Bernstein-von Mises theorems for the behavior of the posterior distribution under both correct and incorrect specification of the conditional moments, subject to growth rate conditions (slower under misspecification) on the number of approximating functions. A large-sample theory for comparing different conditional moment models is also developed. The central result is that the marginal likelihood criterion selects the model that is less misspecified. We also introduce sparsity-based model search for high-dimensional conditioning variables, and provide efficient MCMC computations for high-dimensional parameters. Along with clarifying examples, the framework is illustrated with real-data applications to risk-factor determination in finance, and causal inference under conditional ignorability.
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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 | Donald, Imbens \ Newey (2003) `Empirical likelihood estimation and consistent tests with conditional moment restrictions', Journal of Econometrics 117(1), 55… | 0.874 | 8 | 2 | 100% |
| 2 | Chib, Shin \ Simoni (2018) `Bayesian estimation and comparison of moment condition models', Journal of the American Statistical Association 113(524), 1656–… self | 0.843 | 3 | 3 | 100% |
| 3 | Schennach (2005) `Bayesian exponentially tilted empirical likelihood', Biometrika 92(1), 31–46 | 0.737 | 3 | 2 | 100% |
| 4 | Kleijn \ van der Vaart (2012) `The Bernstein-von-Mises theorem under misspecification', Electronic Journal of Statistics 6, 354–381 | 0.737 | 3 | 2 | 100% |
| 5 | Chamberlain (1987) `Asymptotic efficiency in estimation with conditional moment restrictions', Journal of Econometrics 34(3), 305–334 | 0.644 | 2 | 2 | 100% |
| 6 | Chib \ Ramamurthy (2010) `Tailored Randomized Block MCMC methods with application to DSGE models', Journal of Econometrics 155(1), 19–38 | 0.644 | 2 | 2 | 100% |
| 7 | Chib \ Greenberg (2010) `Additive cubic spline regression with Dirichlet process mixture errors', Journal of Econometrics 156(2), 322–336 | 0.511 | 2 | 1 | 100% |
| 8 | Newey (1997) `Convergence rates and asymptotic normality for series estimators', Journal of Econometrics 79(1), 147 – 168 | 0.511 | 2 | 1 | 100% |
| 9 | Ai \ Chen (2007) `Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables'… | 0.405 | 1 | 1 | 100% |
| 10 | Ai \ Chen (2003) `Efficient estimation of models with conditional moment restrictions containing unknown functions', Econometrica 71(6), 1795–1843 | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 33 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Semiparametric Bayesian Inference for a Conditional Moment Equality Model | 0.894 | 7 | 3 |
| 2 | Generalized Bayes in Conditional Moment Restriction Models | 0.405 | 1 | 1 |
| 3 | High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods | 0.000 | 1 | 1 |