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Imputed quantile tensor regression for near-sited spatial-temporal data

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  • Liang, Jinwen
  • Härdle, Wolfgang Karl
  • Tian, Maozai

Abstract

Modern spatial temporal data are collected from sensor networks. Missing data problems are common for this kind of data. Making robust and accurate imputation is important in many applications. There are complex correlations in both spatial and temporal dimensions. Thus, it is even a challenge to model missing spatial-temporal data. In this article, the imputation of missing values is with the help of related covariates. First, we transform the original sensor × time observational matrix to a high order tensor by adding an extra temporal dimension. Then we integrate quantile tensor regression with tensor completion. The objective function includes check loss and nuclear norm penalty. An alternating update algorithm combined with alternating direction method of multipliers (ADMM) is developed to solve the objective function. Theoretical properties of the proposed estimator are investigated. Simulation studies show our proposed method is more robust and can get more accurate imputation results. Real data analysis about Beijing's PM2.5 concentration level is conducted to verify the efficiency of the estimation procedure.

Suggested Citation

  • Liang, Jinwen & Härdle, Wolfgang Karl & Tian, Maozai, 2023. "Imputed quantile tensor regression for near-sited spatial-temporal data," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:csdana:v:182:y:2023:i:c:s0167947323000245
    DOI: 10.1016/j.csda.2023.107713
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    References listed on IDEAS

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    1. Yu, Jihai & de Jong, Robert & Lee, Lung-fei, 2008. "Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large," Journal of Econometrics, Elsevier, vol. 146(1), pages 118-134, September.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
    4. Peisong Han & Linglong Kong & Jiwei Zhao & Xingcai Zhou, 2019. "A general framework for quantile estimation with incomplete data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 305-333, April.
    5. Su, Liangjun & Yang, Zhenlin, 2015. "QML estimation of dynamic panel data models with spatial errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 230-258.
    6. Lexin Li & Xin Zhang, 2017. "Parsimonious Tensor Response Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1131-1146, July.
    7. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    8. Yang, Zhenlin, 2018. "Unified M-estimation of fixed-effects spatial dynamic models with short panels," Journal of Econometrics, Elsevier, vol. 205(2), pages 423-447.
    9. Yue, Yu Ryan & Rue, Håvard, 2011. "Bayesian inference for additive mixed quantile regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 84-96, January.
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