IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v191y2024ics0167947323002013.html
   My bibliography  Save this article

Nonparametric augmented probability weighting with sparsity

Author

Listed:
  • He, Xin
  • Mao, Xiaojun
  • Wang, Zhonglei

Abstract

Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity score weighting usually leads to estimation inefficiency and introduces a large variability without consideration of sparsity. In this paper, we propose a nonparametric imputation method with sparsity to estimate the finite population mean, where an efficient kernel-based method in the reproducing kernel Hilbet space is employed for estimation and sparse learning. Moreover, an augmented inverse probability weighting framework is adopted to achieve a central limit theorem for the proposed estimator under regularity conditions. The performance of the proposed method is also supported by several simulated examples and one real-life analysis.

Suggested Citation

  • He, Xin & Mao, Xiaojun & Wang, Zhonglei, 2024. "Nonparametric augmented probability weighting with sparsity," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:csdana:v:191:y:2024:i:c:s0167947323002013
    DOI: 10.1016/j.csda.2023.107890
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947323002013
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2023.107890?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Alberto Abadie & Guido W. Imbens, 2016. "Matching on the Estimated Propensity Score," Econometrica, Econometric Society, vol. 84, pages 781-807, March.
    3. Peisong Han & Lu Wang, 2013. "Estimation with missing data: beyond double robustness," Biometrika, Biometrika Trust, vol. 100(2), pages 417-430.
    4. Bryan S. Graham & Cristine Campos De Xavier Pinto & Daniel Egel, 2012. "Inverse Probability Tilting for Moment Condition Models with Missing Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 1053-1079.
    5. M.‐H. Chen & J. G. Ibrahim & C. Yiannoutsos, 1999. "Prior elicitation, variable selection and Bayesian computation for logistic regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 223-242.
    6. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, November.
    7. 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.
    8. Wooldridge, Jeffrey M., 2007. "Inverse probability weighted estimation for general missing data problems," Journal of Econometrics, Elsevier, vol. 141(2), pages 1281-1301, December.
    9. Shu Yang & Jae Kwang Kim & Rui Song, 2020. "Doubly robust inference when combining probability and non‐probability samples with high dimensional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(2), pages 445-465, April.
    10. Yang Ning & Peng Sida & Kosuke Imai, 2020. "Robust estimation of causal effects via a high-dimensional covariate balancing propensity score," Biometrika, Biometrika Trust, vol. 107(3), pages 533-554.
    11. Xiangyu Wang & Chenlei Leng, 2016. "High dimensional ordinary least squares projection for screening variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 589-611, June.
    12. 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.
    13. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    14. Lin, Huazhen & Zhou, Fanyin & Wang, Qiuxia & Zhou, Ling & Qin, Jing, 2018. "Robust and efficient estimation for the treatment effect in causal inference and missing data problems," Journal of Econometrics, Elsevier, vol. 205(2), pages 363-380.
    15. 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.
    16. Kenji Fukumizu & Chenlei Leng, 2014. "Gradient-Based Kernel Dimension Reduction for Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 359-370, March.
    17. Qu, Annie & Lindsay, Bruce G. & Lu, Lin, 2010. "Highly Efficient Aggregate Unbiased Estimating Functions Approach for Correlated Data With Missing at Random," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 194-204.
    18. Valerie C. Bradley & Shiro Kuriwaki & Michael Isakov & Dino Sejdinovic & Xiao-Li Meng & Seth Flaxman, 2021. "Unrepresentative big surveys significantly overestimated US vaccine uptake," Nature, Nature, vol. 600(7890), pages 695-700, December.
    19. Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
    20. Jing Qin & Biao Zhang & Denis H.Y. Leung, 2017. "Efficient Augmented Inverse Probability Weighted Estimation in Missing Data Problems," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 86-97, January.
    21. 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.
    22. Xiaotong Shen & Wei Pan & Yunzhang Zhu & Hui Zhou, 2013. "On constrained and regularized high-dimensional regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 807-832, October.
    23. Wang, Hansheng, 2009. "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1512-1524.
    24. Xiaotong Shen & Wei Pan & Yunzhang Zhu, 2012. "Likelihood-Based Selection and Sharp Parameter Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 223-232, March.
    25. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dai, Linlin & Chen, Kani & Sun, Zhihua & Liu, Zhenqiu & Li, Gang, 2018. "Broken adaptive ridge regression and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 334-351.
    2. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    3. Zhang, Shucong & Zhou, Yong, 2018. "Variable screening for ultrahigh dimensional heterogeneous data via conditional quantile correlations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 1-13.
    4. Xiangyu Wang & Chenlei Leng, 2016. "High dimensional ordinary least squares projection for screening variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 589-611, June.
    5. He, Kevin & Kang, Jian & Hong, Hyokyoung G. & Zhu, Ji & Li, Yanming & Lin, Huazhen & Xu, Han & Li, Yi, 2019. "Covariance-insured screening," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 100-114.
    6. Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    7. Zhao, Bangxin & Liu, Xin & He, Wenqing & Yi, Grace Y., 2021. "Dynamic tilted current correlation for high dimensional variable screening," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    8. He, Yong & Zhang, Liang & Ji, Jiadong & Zhang, Xinsheng, 2019. "Robust feature screening for elliptical copula regression model," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 568-582.
    9. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    10. 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.
    11. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    12. Gabriel E Hoffman & Benjamin A Logsdon & Jason G Mezey, 2013. "PUMA: A Unified Framework for Penalized Multiple Regression Analysis of GWAS Data," PLOS Computational Biology, Public Library of Science, vol. 9(6), pages 1-19, June.
    13. Dong, Yuexiao & Yu, Zhou & Zhu, Liping, 2020. "Model-free variable selection for conditional mean in regression," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    14. Akira Shinkyu, 2023. "Forward Selection for Feature Screening and Structure Identification in Varying Coefficient Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 485-511, February.
    15. Howard D. Bondell & Brian J. Reich, 2012. "Consistent High-Dimensional Bayesian Variable Selection via Penalized Credible Regions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1610-1624, December.
    16. Yanhang Zhang & Junxian Zhu & Jin Zhu & Xueqin Wang, 2023. "A Splicing Approach to Best Subset of Groups Selection," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 104-119, January.
    17. Zhihua Sun & Yi Liu & Kani Chen & Gang Li, 2022. "Broken adaptive ridge regression for right-censored survival data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 69-91, February.
    18. Zhou Yu & Yuexiao Dong & Li-Xing Zhu, 2016. "Trace Pursuit: A General Framework for Model-Free Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 813-821, April.
    19. Shanshan Qin & Hao Ding & Yuehua Wu & Feng Liu, 2021. "High-dimensional sign-constrained feature selection and grouping," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 787-819, August.
    20. Canhong Wen & Xueqin Wang & Shaoli Wang, 2015. "Laplace Error Penalty-based Variable Selection in High Dimension," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 685-700, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:191:y:2024:i:c:s0167947323002013. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.