Jinyuan Chang, Cheng Yong Tang, Yuanzheng Zhu
arXiv 23 Dec 2024 · Statistics — Methodology · publishedJournal of the Royal Statistical Society Series B (Statistical Methodology) (2025)
arXiv:2412.17354 · PDF · DOI · OpenAlex · Extracted main text
In this study, we introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two primary objectives: (i) to enhance the inherent flexibility of EL in accommodating diverse model conditions, and (ii) to facilitate the use of well-established Markov Chain Monte Carlo (MCMC) sampling schemes as a convenient alternative to the complex optimization typically required for statistical inference using EL. To achieve the first objective, we propose a penalized approach that regularizes the Lagrange multipliers, significantly reducing the dimensionality of the problem while accommodating a comprehensive set of model conditions. For the second objective, our study designs and thoroughly investigates two popular sampling schemes within the BPEL context. We demonstrate that the BPEL framework is highly flexible and efficient, enhancing the adaptability and practicality of EL methods. Our study highlights the practical advantages of using sampling techniques over traditional optimization methods for EL problems, showing rapid convergence to the global optima of posterior distributions and ensuring the effective resolution of complex statistical inference challenges.
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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 | Shi, Z (2016) Econometric estimation with high-dimensional moment equalities | 1.000 | 8 | 4 | 100% |
| 2 | Mengersen, K. L., Pudlo, P., & Robert, C. P (2013) Bayesian computation via empirical likelihood | 0.843 | 3 | 3 | 100% |
| 3 | Cornuet, J.-M., Marin, J.-M., Mira, A., & Robert, C. P (2012) Adaptive multiple importance sampling | 0.737 | 3 | 2 | 100% |
| 4 | Chaussé, P (2017) Generalized empirical likelihood for a continuum of moment conditions | 0.737 | 3 | 2 | 100% |
| 5 | Hsu, D., Kakade, S. M., & Zhang, T (2012) A tail inequality for quadratic forms of subgaussian random vectors | 0.737 | 3 | 2 | 100% |
| 6 | Jing, B. Y., Shao, Q. M., & Wang, Q (2003) Self-normalized cramer-type large deviations for independent random variables | 0.737 | 3 | 2 | 100% |
| 7 | Ma, Y.-A., Chen, Y., Jin, C., Flammarion, N., & Jordan, M. I (2019) Sampling can be faster than optimization | 0.737 | 3 | 2 | 100% |
| 8 | Chang, J., Tang, C. Y., & Wu, T (2018) A new scope of penalized empirical likelihood with high-dimensional estimating equations self | 0.693 | 6 | 1 | 100% |
| 9 | Chang, J., Chen, S. X., & Chen, X (2015) High dimensional generalized empirical likelihood for moment restrictions with dependent data self | 0.644 | 2 | 2 | 100% |
| 10 | Chang, J., Tang, C. Y., & Wu, T (2018) A new scope of penalized empirical likelihood with high-dimensional estimating equations self | 0.644 | 2 | 2 | 100% |
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