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Distributed simultaneous inference in generalized linear models via confidence distribution

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  • Tang, Lu
  • Zhou, Ling
  • Song, Peter X.-K.

Abstract

We propose a distributed method for simultaneous inference for datasets with sample size much larger than the number of covariates, i.e., N≫p, in the generalized linear models framework. When such datasets are too big to be analyzed entirely by a single centralized computer, or when datasets are already stored in distributed database systems, the strategy of divide-and-combine has been the method of choice for scalability. Due to partition, the sub-dataset sample sizes may be uneven and some possibly close to p, which calls for regularization techniques to improve numerical stability. However, there is a lack of clear theoretical justification and practical guidelines to combine results obtained from separate regularized estimators, especially when the final objective is simultaneous inference for a group of regression parameters. In this paper, we develop a strategy to combine bias-corrected lasso-type estimates by using confidence distributions. We show that the resulting combined estimator achieves the same estimation efficiency as that of the maximum likelihood estimator using the centralized data. As demonstrated by simulated and real data examples, our divide-and-combine method yields nearly identical inference as the centralized benchmark.

Suggested Citation

  • Tang, Lu & Zhou, Ling & Song, Peter X.-K., 2020. "Distributed simultaneous inference in generalized linear models via confidence distribution," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
  • Handle: RePEc:eee:jmvana:v:176:y:2020:i:c:s0047259x1930065x
    DOI: 10.1016/j.jmva.2019.104567
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    References listed on IDEAS

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    Cited by:

    1. Changgee Chang & Zhiqi Bu & Qi Long, 2023. "CEDAR: communication efficient distributed analysis for regressions," Biometrics, The International Biometric Society, vol. 79(3), pages 2357-2369, September.
    2. Lu Lin & Feng Li, 2023. "Global debiased DC estimations for biased estimators via pro forma regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 726-758, June.
    3. Wei Wang & Shou‐En Lu & Jerry Q. Cheng & Minge Xie & John B. Kostis, 2022. "Multivariate survival analysis in big data: A divide‐and‐combine approach," Biometrics, The International Biometric Society, vol. 78(3), pages 852-866, September.
    4. Nezakati, Ensiyeh & Pircalabelu, Eugen, 2021. "Unbalanced distributed estimation and inference for precision matrices," LIDAM Discussion Papers ISBA 2021031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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