Bayesian Empirical Likelihood Inference with Complex Survey Data

Zhao, Puying; Ghosh, Malay; Rao, J. N. K.; Wu, Changbao

doi:10.1111/rssb.12342

Cited by 22 publications

(14 citation statements)

References 42 publications

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“…First, a Bayesian approach can be developed under the same setup. One may use the Bayesian empirical likelihood method of Zhao et al (2020) in this setup. The proposed method can potentially be used to combine the randomized clinical trial data with big real-world data ; such extensions will be presented elsewhere.…”

Section: Discussionmentioning

confidence: 99%

Survey data integration for regression analysis using model calibration

Wang¹,

J.²,

Kim³

2021

Preprint

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We consider regression analysis in the context of data integration. To combine partial information from external sources, we employ the idea of model calibration which introduces a "working" reduced model based on the observed covariates. The working reduced model is not necessarily correctly specified but can be a useful device to incorporate the partial information from the external data. The actual implementation is based on a novel application of the empirical likelihood method. The proposed method is particularly attractive for combining information from several sources with different missing patterns. The proposed method is applied to a real data example combining survey data from Korean National Health and Nutrition Examination Survey and big data from National Health Insurance Sharing Service in Korea.

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Section: Discussionmentioning

confidence: 99%

Survey data integration for regression analysis using model calibration

Wang¹,

J.²,

Kim³

2021

Preprint

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“…Specifically, in a shrinking neighborhood of ρ 1/2 n x 0i with radius n , condition (4.2) requires that the negative Hessian of (1/n) in is close to a deterministic d × d positive definite matrix Σ in , and condition (4.3) guarantees that in is strongly concave in a larger shrinking neighborhood of ρ 1/2 n x 0i with radius 3δ n . Finally, condition (4.4) is an identifiability condition for the criterion function, which is standard in the literature on generalized Bayesian estimation (see, for example, Chernozhukov and Hong, 2003;Chib et al, 2018;Yiu et al, 2020;Zhao et al, 2020).…”

Section: Convergence Of the Generalized Posteriormentioning

confidence: 99%

Eigenvector-Assisted Statistical Inference for Signal-Plus-Noise Matrix Models

Xie¹,

Wu²

2022

Preprint

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In this paper, we develop a generalized Bayesian inference framework for a collection of signal-plusnoise matrix models arising in high-dimensional statistics and many applications. The framework is built upon an asymptotically unbiased estimating equation with the assistance of the leading eigenvectors of the data matrix. The solution to the estimating equation coincides with the maximizer of an appropriate statistical criterion function. The generalized posterior distribution is constructed by replacing the usual log-likelihood function in the Bayes formula with the criterion function. The proposed framework does not require the complete specification of the sampling distribution and is convenient for uncertainty quantification via a Markov Chain Monte Carlo sampler, circumventing the inconvenience of resampling the data matrix. Under mild regularity conditions, we establish the large sample properties of the estimating equation estimator and the generalized posterior distributions. In particular, the generalized posterior credible sets have the correct frequentist nominal coverage probability provided that the socalled generalized information equality holds. The validity and usefulness of the proposed framework are demonstrated through the analysis of synthetic datasets and the real-world ENZYMES network datasets.

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“…which is routinely applied in the analysis of survey data. There are many studies on this estimator in design-based context; see, e.g., Chauvet (2015), Berger and De La Riva Torres (2016), Chauvet and Vallée (2020), Zhao et al (2020), and references therein. To adapt the asymptotic theory in the last section, here we take the model-based approach based on a hypothetical infinite population (Fisher, 1922).…”

Section: Generalizationsmentioning

confidence: 99%

Multiway empirical likelihood

Chiang¹,

Matsushita²,

Otsu³

2021

Preprint

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This paper develops a general methodology to conduct statistical inference for observations indexed by multiple sets of entities. We propose a novel multiway empirical likelihood statistic that converges to a chi-square distribution under the non-degenerate case, where corresponding Hoeffding type decomposition is dominated by linear terms. Our methodology is related to the notion of jackknife empirical likelihood but the leave-out pseudo values are constructed by leaving columns or rows. We further develop a modified version of our multiway empirical likelihood statistic, which converges to a chi-square distribution regardless of the degeneracy. The proposed methodology is illustrated by several important statistical problems, such as bipartite network, two-stage sampling, generalized estimating equations, and three-way observations. Simulations under various settings confirm its desirable performances.

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Bayesian Empirical Likelihood Inference with Complex Survey Data

Cited by 22 publications

References 42 publications

Survey data integration for regression analysis using model calibration

Survey data integration for regression analysis using model calibration

Eigenvector-Assisted Statistical Inference for Signal-Plus-Noise Matrix Models

Multiway empirical likelihood

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