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Statistical inference in massive data sets

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  • Runze Li
  • Dennis K.J. Lin
  • Bing Li

Abstract

Analysis of massive data sets is challenging owing to limitations of computer primary memory. In this paper, we propose an approach to estimate population parameters from a massive data set. The proposed approach significantly reduces the required amount of primary memory, and the resulting estimate will be as efficient if the entire data set was analyzed simultaneously. Asymptotic properties of the resulting estimate are studied, and the asymptotic normality of the resulting estimator is established. The standard error formula for the resulting estimate is proposed and empirically tested; thus, statistical inference for parameters of interest can be performed. The effectiveness of the proposed approach is illustrated using simulation studies and an Internet traffic data example. Copyright © 2012 John Wiley & Sons, Ltd.

Suggested Citation

  • Runze Li & Dennis K.J. Lin & Bing Li, 2013. "Statistical inference in massive data sets," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(5), pages 399-409, September.
    • Handle: RePEc:wly:apsmbi:v:29:y:2013:i:5:p:399-409
    DOI: 10.1002/asmb.1927
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    Cited by:

    1. Fengrui Di & Lei Wang, 2022. "Multi-round smoothed composite quantile regression for distributed data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 869-893, October.
    2. Xuejun Ma & Shaochen Wang & Wang Zhou, 2022. "Statistical inference in massive datasets by empirical likelihood," Computational Statistics, Springer, vol. 37(3), pages 1143-1164, July.
    3. Samya Tajmouati & Bouazza El Wahbi & Mohamed Dakkon, 2023. "Classical and fast parameters tuning in nearest neighbors with stop condition," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1063-1081, September.
    4. 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.
    5. Luo, Jiyu & Sun, Qiang & Zhou, Wen-Xin, 2022. "Distributed adaptive Huber regression," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    6. Nguyen, Hien D. & McLachlan, Geoffrey J., 2018. "Chunked-and-averaged estimators for vector parameters," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 336-342.
    7. Chen, Lanjue & Zhou, Yong, 2020. "Quantile regression in big data: A divide and conquer based strategy," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    8. Jiang, Rong & Yu, Keming, 2020. "Single-index composite quantile regression for massive data," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    9. Rong Jiang & Wei-wei Chen & Xin Liu, 2021. "Adaptive quantile regressions for massive datasets," Statistical Papers, Springer, vol. 62(4), pages 1981-1995, August.
    10. Andrew Morgan & Alan Dix & Mike Phillips & Chris House, 2014. "Blue sky thinking meets green field usability: Can mobile internet software engineering bridge the rural divide?," Local Economy, London South Bank University, vol. 29(6-7), pages 750-761, September.
    11. Qifa Xu & Chao Cai & Cuixia Jiang & Fang Sun & Xue Huang, 2020. "Block average quantile regression for massive dataset," Statistical Papers, Springer, vol. 61(1), pages 141-165, February.
    12. Flisi, Sara & Goglio, Valentina & Meroni, Elena Claudia & Vera-Toscano, Esperanza, 2019. "Cohort patterns in adult literacy skills: How are new generations doing?," Journal of Policy Modeling, Elsevier, vol. 41(1), pages 52-65.
    13. Lawal, Abiola S. & Servadio, Joseph L. & Davis, Tate & Ramaswami, Anu & Botchwey, Nisha & Russell, Armistead G., 2021. "Orthogonalization and machine learning methods for residential energy estimation with social and economic indicators," Applied Energy, Elsevier, vol. 283(C).
    14. Runmin Shi & Faming Liang & Qifan Song & Ye Luo & Malay Ghosh, 2018. "A Blockwise Consistency Method for Parameter Estimation of Complex Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 179-223, December.

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