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Semi-profiled distributed estimation for high-dimensional partially linear model

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  • Bao, Yajie
  • Ren, Haojie

Abstract

As a leading example in the semiparametric model, the partially linear model is prominent in modeling complex data. The challenges associated with designing an efficient estimation algorithm in the distributed environment are not yet well addressed. The existing works require a constraint on the number of local machines to guarantee the optimality of the global estimator. In addition, a multi-round profiled estimator will lead to huge communication complexity. To further reduce communication costs, a novel semi-profiled estimation procedure is proposed, which provides an iterative skeleton to reduce estimation error. A new multi-round distributed algorithm based on the centralized semi-profiled estimator is developed, which can estimate the parametric and nonparametric simultaneously. The theoretical results indicate that the corresponding convergence rates can achieve the optimal orders within a constant number of communication rounds. The advantages of the proposed estimation method are demonstrated via numerical experiments on synthetic and real data.

Suggested Citation

  • Bao, Yajie & Ren, Haojie, 2023. "Semi-profiled distributed estimation for high-dimensional partially linear model," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:csdana:v:188:y:2023:i:c:s0167947323001354
    DOI: 10.1016/j.csda.2023.107824
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    References listed on IDEAS

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    1. Xi Chen & Jason D. Lee & He Li & Yun Yang, 2022. "Distributed Estimation for Principal Component Analysis: An Enlarged Eigenspace Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1775-1786, October.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. Jianqing Fan & Yunbei Ma & Wei Dai, 2014. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1270-1284, September.
    4. Wang, Yue & Zhou, Yan & Li, Rui & Lian, Heng, 2022. "Sparse high-dimensional semi-nonparametric quantile regression in a reproducing kernel Hilbert space," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    5. Liang, Hua & Li, Runze, 2009. "Variable Selection for Partially Linear Models With Measurement Errors," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 234-248.
    6. Michael I. Jordan & Jason D. Lee & Yun Yang, 2019. "Communication-Efficient Distributed Statistical Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 668-681, April.
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