IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v62y2021i6d10.1007_s00362-020-01208-x.html
   My bibliography  Save this article

Global statistical inference for the difference between two regression mean curves with covariates possibly partially missing

Author

Listed:
  • Li Cai

    (Zhejiang Gongshang University)

  • Suojin Wang

    (Texas A&M University)

Abstract

In two sample problems it is of interest to examine the difference between the two regression curves or to detect whether certain functions are adequate to describe the overall trend of the difference. In this paper, we propose a simultaneous confidence band (SCB) as a global inference method with asymptotically correct coverage probabilities for the difference curve based on the weighted local linear kernel regression estimates in each sample. Our procedure allows for random designs, different sample sizes, heteroscedastic errors, and especially missing covariates. Simulation studies are conducted to investigate the finite sample properties of the new SCB which support our asymptotic theory. The proposed SCB is used to analyze two data sets, one of which is concerned with human event-related potentials data which are fully observed and the other is concerned with the Canada 2010/2011 youth student survey data with partially missing covariates, leading to a number of discoveries.

Suggested Citation

  • Li Cai & Suojin Wang, 2021. "Global statistical inference for the difference between two regression mean curves with covariates possibly partially missing," Statistical Papers, Springer, vol. 62(6), pages 2573-2602, December.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:6:d:10.1007_s00362-020-01208-x
    DOI: 10.1007/s00362-020-01208-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-020-01208-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-020-01208-x?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. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    2. Majid Mojirsheibani & Timothy Reese, 2017. "Kernel regression estimation for incomplete data with applications," Statistical Papers, Springer, vol. 58(1), pages 185-209, March.
    3. L. Baringhaus & D. Kolbe, 2015. "Two-sample tests based on empirical Hankel transforms," Statistical Papers, Springer, vol. 56(3), pages 597-617, August.
    4. Johnston, Gordon J., 1982. "Probabilities of maximal deviations for nonparametric regression function estimates," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 402-414, September.
    5. Paolo Cozzucoli, 2010. "Simultaneous confidence intervals on partial means of classes in the two-stage stratified sampling," Statistical Papers, Springer, vol. 51(3), pages 673-685, September.
    6. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    7. Xuemin Zi & Changliang Zou & Yukun Liu, 2012. "Two-sample empirical likelihood method for difference between coefficients in linear regression model," Statistical Papers, Springer, vol. 53(1), pages 83-93, February.
    8. Zhou Zhou & Wei Biao Wu, 2010. "Simultaneous inference of linear models with time varying coefficients," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 513-531, September.
    9. Hall, Peter & Titterington, D. M., 1988. "On confidence bands in nonparametric density estimation and regression," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 228-254, October.
    10. Qiongxia Song & Lijian Yang, 2009. "Spline confidence bands for variance functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 589-609.
    11. Li Cai & Lijian Yang, 2015. "A smooth simultaneous confidence band for conditional variance function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 632-655, September.
    12. G. I. Rivas-Martínez & M. D. Jiménez-Gamero & J. L. Moreno-Rebollo, 2019. "A two-sample test for the error distribution in nonparametric regression based on the characteristic function," Statistical Papers, Springer, vol. 60(4), pages 1369-1395, August.
    13. Li Cai & Lisha Li & Simin Huang & Liang Ma & Lijian Yang, 2020. "Oracally efficient estimation for dense functional data with holiday effects," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 282-306, March.
    14. Guanqun Cao & Lijian Yang & David Todem, 2012. "Simultaneous inference for the mean function based on dense functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 359-377.
    15. Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410, June.
    16. Natalie Neumeyer & Stefan Sperlich, 2006. "Comparison of Separable Components in Different Samples," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 477-501, September.
    17. Zhao, Shi & Bakoyannis, Giorgos & Lourens, Spencer & Tu, Wanzhu, 2020. "Comparison of nonlinear curves and surfaces," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    18. T. Tony Cai & Mark Low & Zongming Ma, 2014. "Adaptive Confidence Bands for Nonparametric Regression Functions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1054-1070, September.
    19. Y. Xia, 1998. "Bias‐corrected confidence bands in nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 797-811.
    20. Sanyu Zhou & Defa Wang & Jingjing Zhu, 2020. "Construction of simultaneous confidence bands for a percentile hyper-plane with predictor variables constrained in an ellipsoidal region," Statistical Papers, Springer, vol. 61(3), pages 1335-1346, 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 Cai & Lijie Gu & Qihua Wang & Suojin Wang, 2021. "Simultaneous confidence bands for nonparametric regression with missing covariate data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1249-1279, December.
    2. Chen Zhong & Lijian Yang, 2021. "Simultaneous confidence bands for comparing variance functions of two samples based on deterministic designs," Computational Statistics, Springer, vol. 36(2), pages 1197-1218, June.
    3. Yuanyuan Zhang & Lijian Yang, 2018. "A smooth simultaneous confidence band for correlation curve," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 247-269, June.
    4. Majid Mojirsheibani, 2022. "On the maximal deviation of kernel regression estimators with NMAR response variables," Statistical Papers, Springer, vol. 63(5), pages 1677-1705, October.
    5. Li Cai & Lisha Li & Simin Huang & Liang Ma & Lijian Yang, 2020. "Oracally efficient estimation for dense functional data with holiday effects," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 282-306, March.
    6. Lijie Gu & Suojin Wang & Lijian Yang, 2019. "Simultaneous confidence bands for the distribution function of a finite population in stratified sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 983-1005, August.
    7. Ali Al-Sharadqah & Majid Mojirsheibani, 2020. "A simple approach to construct confidence bands for a regression function with incomplete data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 81-99, March.
    8. Degui Li & Bin Peng & Songqiao Tang & Weibiao Wu, 2023. "Inference of Grouped Time-Varying Network Vector Autoregression Models," Monash Econometrics and Business Statistics Working Papers 5/23, Monash University, Department of Econometrics and Business Statistics.
    9. Jiaqi Li & Likai Chen & Kun Ho Kim & Tianwei Zhou, 2022. "Simultaneous Inference of a Partially Linear Model in Time Series," Papers 2212.10359, arXiv.org, revised Sep 2023.
    10. Jie Li & Jiangyan Wang & Lijian Yang, 2022. "Kolmogorov–Smirnov simultaneous confidence bands for time series distribution function," Computational Statistics, Springer, vol. 37(3), pages 1015-1039, July.
    11. G. I. Rivas-Martínez & M. D. Jiménez-Gamero & J. L. Moreno-Rebollo, 2019. "A two-sample test for the error distribution in nonparametric regression based on the characteristic function," Statistical Papers, Springer, vol. 60(4), pages 1369-1395, August.
    12. Gu, Lijie & Wang, Suojin & Yang, Lijian, 2021. "Smooth simultaneous confidence band for the error distribution function in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    13. Stefan Sperlich, 2014. "On the choice of regularization parameters in specification testing: a critical discussion," Empirical Economics, Springer, vol. 47(2), pages 427-450, September.
    14. Degui Li & Bin Peng & Songqiao Tang & Weibiao Wu, 2023. "Estimation of Grouped Time-Varying Network Vector Autoregression Models," Papers 2303.10117, arXiv.org, revised Mar 2024.
    15. Liugen Xue, 2010. "Empirical Likelihood Local Polynomial Regression Analysis of Clustered Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 644-663, December.
    16. Pedro H. C. Sant'Anna & Xiaojun Song & Qi Xu, 2022. "Covariate distribution balance via propensity scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1093-1120, September.
    17. Kim, Kun Ho & Chao, Shih-Kang & Härdle, Wolfgang Karl, 2020. "Simultaneous Inference of the Partially Linear Model with a Multivariate Unknown Function," IRTG 1792 Discussion Papers 2020-008, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    18. Weichi Wu & Zhou Zhou, 2017. "Nonparametric Inference for Time-Varying Coefficient Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 98-109, January.
    19. Adam D. Bull, 2015. "Semimartingale detection and goodness-of-fit tests," Papers 1506.00088, arXiv.org, revised Jun 2016.
    20. Dong, Hao & Taylor, Luke, 2022. "Nonparametric Significance Testing In Measurement Error Models," Econometric Theory, Cambridge University Press, vol. 38(3), pages 454-496, June.

    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:spr:stpapr:v:62:y:2021:i:6:d:10.1007_s00362-020-01208-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.