IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v188y2022ics0047259x21000968.html
   My bibliography  Save this article

Independence tests in the presence of measurement errors: An invariance law

Author

Listed:
  • Fan, Jinlin
  • Zhang, Yaowu
  • Zhu, Liping

Abstract

In many scientific areas the observations are collected with measurement errors. We are interested in measuring and testing independence between random vectors which are subject to measurement errors. We modify the weight functions in the classic distance covariance such that, the modified distance covariance between the random vectors of primary interest is the same as its classic version between the surrogate random vectors, which is referred to as the invariance law in the present context. The presence of measurement errors may substantially weaken the degree of nonlinear dependence. An immediate issue arises: The classic distance correlation between the surrogate vectors cannot reach one even if the two random vectors of primary interest are exactly linearly dependent. To address this issue, we propose to estimate the distance variance using repeated measurements. We study the asymptotic properties of the modified distance correlation thoroughly. In addition, we demonstrate its finite-sample performance through extensive simulations and a real-world application.

Suggested Citation

  • Fan, Jinlin & Zhang, Yaowu & Zhu, Liping, 2022. "Independence tests in the presence of measurement errors: An invariance law," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:jmvana:v:188:y:2022:i:c:s0047259x21000968
    DOI: 10.1016/j.jmva.2021.104818
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X21000968
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2021.104818?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. Wang, Yining & Wang, Jialei & Balakrishnan, Sivaraman & Singh, Aarti, 2019. "Rate optimal estimation and confidence intervals for high-dimensional regression with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    2. Alexandre Belloni & Victor Chernozhukov & Abhishek Kaul, 2017. "Confidence bands for coefficients in high dimensional linear models with error-in-variables," CeMMAP working papers 22/17, Institute for Fiscal Studies.
    3. Chi-Lun Cheng & Chih-Ling Tsai, 2004. "The Invariance of Some Score Tests in the Linear Model With Classical Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 805-809, January.
    4. Liping Zhu & Kai Xu & Runze Li & Wei Zhong, 2017. "Projection correlation between two random vectors," Biometrika, Biometrika Trust, vol. 104(4), pages 829-843.
    5. Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
    6. Li, Mengyan & Li, Runze & Ma, Yanyuan, 2021. "Inference in high dimensional linear measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    7. 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.
    8. Li-Pang Chen, 2021. "Feature screening based on distance correlation for ultrahigh-dimensional censored data with covariate measurement error," Computational Statistics, Springer, vol. 36(2), pages 857-884, June.
    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. Li, Mengyan & Li, Runze & Ma, Yanyuan, 2021. "Inference in high dimensional linear measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    2. Zhou, Yeqing & Liu, Jingyuan & Zhu, Liping, 2020. "Test for conditional independence with application to conditional screening," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    3. Mirosław Krzyśko & Łukasz Smaga, 2024. "Application of distance standard deviation in functional data analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(2), pages 431-454, June.
    4. Cencheng Shen & Joshua T. Vogelstein, 2021. "The exact equivalence of distance and kernel methods in hypothesis testing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 385-403, September.
    5. Liu, Jicai & Si, Yuefeng & Niu, Yong & Zhang, Riquan, 2022. "Projection quantile correlation and its use in high-dimensional grouped variable screening," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    6. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Jing Zhang & Qihua Wang & Xuan Wang, 2022. "Surrogate-variable-based model-free feature screening for survival data under the general censoring mechanism," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 379-397, April.
    8. Zhaoyu Xing & Yang Wan & Juan Wen & Wei Zhong, 2024. "GOLFS: feature selection via combining both global and local information for high dimensional clustering," Computational Statistics, Springer, vol. 39(5), pages 2651-2675, July.
    9. Xia Chen & Liyue Mao, 2020. "Penalized empirical likelihood for partially linear errors-in-variables models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 597-623, December.
    10. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    11. Linh H. Nghiem & Francis K.C. Hui & Samuel Müller & A.H. Welsh, 2023. "Screening methods for linear errors‐in‐variables models in high dimensions," Biometrics, The International Biometric Society, vol. 79(2), pages 926-939, June.
    12. Hung Hung & Su‐Yun Huang, 2019. "Sufficient dimension reduction via random‐partitions for the large‐p‐small‐n problem," Biometrics, The International Biometric Society, vol. 75(1), pages 245-255, March.
    13. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    14. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    15. Jingyuan Liu & Runze Li & Rongling Wu, 2014. "Feature Selection for Varying Coefficient Models With Ultrahigh-Dimensional Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 266-274, March.
    16. Alexandre Belloni & Victor Chernozhukov & Abhishek Kaul, 2017. "Confidence bands for coefficients in high dimensional linear models with error-in-variables," CeMMAP working papers CWP22/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Zhang, Jing & Wang, Qihua & Kang, Jian, 2020. "Feature screening under missing indicator imputation with non-ignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    18. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    19. Zhang, Qingyang, 2019. "Independence test for large sparse contingency tables based on distance correlation," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 17-22.
    20. Lu, Jun & Lin, Lu, 2018. "Feature screening for multi-response varying coefficient models with ultrahigh dimensional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 242-254.

    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:jmvana:v:188:y:2022:i:c:s0047259x21000968. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.