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Overview of High-Dimensional Measurement Error Regression Models

Author

Listed:
  • Jingxuan Luo

    (School of Statistics, Beijing Normal University, Beijing 100875, China)

  • Lili Yue

    (School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China)

  • Gaorong Li

    (School of Statistics, Beijing Normal University, Beijing 100875, China)

Abstract

High-dimensional measurement error data are becoming more prevalent across various fields. Research on measurement error regression models has gained momentum due to the risk of drawing inaccurate conclusions if measurement errors are ignored. When the dimension p is larger than the sample size n , it is challenging to develop statistical inference methods for high-dimensional measurement error regression models due to the existence of bias, nonconvexity of the objective function, high computational cost and many other difficulties. Over the past few years, some works have overcome the aforementioned difficulties and proposed several novel statistical inference methods. This paper mainly reviews the current development on estimation, hypothesis testing and variable screening methods for high-dimensional measurement error regression models and shows the theoretical results of these methods with some directions worthy of exploring in future research.

Suggested Citation

  • Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3202-:d:1199385
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    References listed on IDEAS

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    1. Wenliang Pan & Xueqin Wang & Weinan Xiao & Hongtu Zhu, 2019. "A Generic Sure Independence Screening Procedure," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 928-937, April.
    2. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    3. Faming Liang & Bochao Jia & Jingnan Xue & Qizhai Li & Ye Luo, 2018. "An imputation–regularized optimization algorithm for high dimensional missing data problems and beyond," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 899-926, November.
    4. Jun Zhang, 2021. "Estimation and variable selection for partial linear single-index distortion measurement errors models," Statistical Papers, Springer, vol. 62(2), pages 887-913, April.
    5. Cui, Hengjian & Chen, Song Xi, 2003. "Empirical likelihood confidence region for parameter in the errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 101-115, January.
    6. Emre Barut & Jianqing Fan & Anneleen Verhasselt, 2016. "Conditional Sure Independence Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1266-1277, July.
    7. Yanyuan Ma & Jeffrey D. Hart & Ryan Janicki & Raymond J. Carroll, 2011. "Local and omnibus goodness‐of‐fit tests in classical measurement error models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 81-98, January.
    8. Simon N. Vandekar & Philip T. Reiss & Russell T. Shinohara, 2019. "Interpretable High-Dimensional Inference Via Score Projection With an Application in Neuroimaging," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 820-830, April.
    9. S. M. Schennach & Yingyao Hu, 2013. "Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 177-186, March.
    10. Alexandre Belloni & Mathieu Rosenbaum & Alexandre B. Tsybakov, 2017. "Linear and conic programming estimators in high dimensional errors-in-variables models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 939-956, June.
    11. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    12. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    13. Liming Wang & Xingxiang Li & Xiaoqing Wang & Peng Lai, 2022. "Unified mean-variance feature screening for ultrahigh-dimensional regression," Computational Statistics, Springer, vol. 37(4), pages 1887-1918, September.
    14. Pixu Shi & Yuchen Zhou & Anru R Zhang, 2022. "High-dimensional log-error-in-variable regression with applications to microbial compositional data analysis [Log contrast models for experiments with mixtures]," Biometrika, Biometrika Trust, vol. 109(2), pages 405-420.
    15. 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.
    16. Staudenmayer, John & Buonaccorsi, John P., 2005. "Measurement Error in Linear Autoregressive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 841-852, September.
    17. Zheng, Zemin & Li, Yang & Yu, Chongxiu & Li, Gaorong, 2018. "Balanced estimation for high-dimensional measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 78-91.
    18. Zhao, Shaofei & Fu, Guifang, 2022. "Distribution-free and model-free multivariate feature screening via multivariate rank distance correlation," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    19. Peter Hall & Yanyuan Ma, 2007. "Semiparametric estimators of functional measurement error models with unknown error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 429-446, June.
    20. Zhenghui Feng & Jun Zhang & Qian Chen, 2020. "Statistical inference for linear regression models with additive distortion measurement errors," Statistical Papers, Springer, vol. 61(6), pages 2483-2509, December.
    21. Gareth M. James & Peter Radchenko, 2009. "A generalized Dantzig selector with shrinkage tuning," Biometrika, Biometrika Trust, vol. 96(2), pages 323-337.
    22. Wei, Ying & Carroll, Raymond J., 2009. "Quantile Regression With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1129-1143.
    23. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    24. Wang, Liqun & Hsiao, Cheng, 2011. "Method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 165(1), pages 30-44.
    25. Wenqin Pan & Donglin Zeng & Xihong Lin, 2009. "Estimation in Semiparametric Transition Measurement Error Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 65(3), pages 728-736, September.
    26. Shujie Ma & Runze Li & Chih-Ling Tsai, 2017. "Variable Screening via Quantile Partial Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 650-663, April.
    27. Xinyu Zhang & Yanyuan Ma & Raymond J. Carroll, 2019. "MALMEM: model averaging in linear measurement error models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(4), pages 763-779, September.
    28. Xianyang Zhang & Guang Cheng, 2017. "Simultaneous Inference for High-Dimensional Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 757-768, April.
    29. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    30. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    31. Carroll, Raymond J. & Delaigle, Aurore & Hall, Peter, 2009. "Nonparametric Prediction in Measurement Error Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 993-1003.
    32. Hengjian Cui & Efang Kong, 2006. "Empirical Likelihood Confidence Region for Parameters in Semi‐linear Errors‐in‐Variables Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 153-168, March.
    33. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    34. Ma, Yanyuan & Carroll, Raymond J., 2006. "Locally Efficient Estimators for Semiparametric Models With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1465-1474, December.
    35. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
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