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Renewable estimation and incremental inference in generalized linear models with streaming data sets

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  • Lan Luo
  • Peter X.‐K. Song

Abstract

The paper presents an incremental updating algorithm to analyse streaming data sets using generalized linear models. The method proposed is formulated within a new framework of renewable estimation and incremental inference, in which the maximum likelihood estimator is renewed with current data and summary statistics of historical data. Our framework can be implemented within a popular distributed computing environment, known as Apache Spark, to scale up computation. Consisting of two data‐processing layers, the rho architecture enables us to accommodate inference‐related statistics and to facilitate sequential updating of the statistics used in both estimation and inference. We establish estimation consistency and asymptotic normality of the proposed renewable estimator, in which the Wald test is utilized for an incremental inference. Our methods are examined and illustrated by various numerical examples from both simulation experiments and a real world data analysis.

Suggested Citation

  • Lan Luo & Peter X.‐K. Song, 2020. "Renewable estimation and incremental inference in generalized linear models with streaming data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(1), pages 69-97, February.
    • Handle: RePEc:bla:jorssb:v:82:y:2020:i:1:p:69-97
    DOI: 10.1111/rssb.12352
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    Cited by:

    1. Jianfeng Wei & Jian Yang & Xuewen Cheng & Jie Ding & Shengquan Li, 2023. "Adaptive Regression Analysis of Heterogeneous Data Streams via Models with Dynamic Effects," Mathematics, MDPI, vol. 11(24), pages 1-18, December.
    2. Liu, Wei & Luo, Lan & Zhou, Ling, 2023. "Online missing value imputation for high-dimensional mixed-type data via generalized factor models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    3. Hector, Emily C. & Luo, Lan & Song, Peter X.-K., 2023. "Parallel-and-stream accelerator for computationally fast supervised learning," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    4. Tianzhen Wang & Haixiang Zhang, 2022. "Optimal subsampling for multiplicative regression with massive data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(4), pages 418-449, November.
    5. Yu Jeffrey Hu & Jeroen Rombouts & Ines Wilms, 2023. "Fast Forecasting of Unstable Data Streams for On-Demand Service Platforms," Papers 2303.01887, arXiv.org, revised May 2024.

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