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Smooth simultaneous confidence bands for cumulative distribution functions

Author

Listed:
  • Jiangyan Wang
  • Fuxia Cheng
  • Lijian Yang

Abstract

A plug-in kernel estimator is proposed for Hölder continuous cumulative distribution function (cdf) based on a random sample. Uniform closeness between the proposed estimator and the empirical cdf estimator is established, while the proposed estimator is smooth instead of a step function. A smooth simultaneous confidence band is constructed based on the smooth distribution estimator and the Kolmogorov distribution. Extensive simulation study using two different automatic bandwidths confirms the theoretical findings.

Suggested Citation

  • Jiangyan Wang & Fuxia Cheng & Lijian Yang, 2013. "Smooth simultaneous confidence bands for cumulative distribution functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 395-407, June.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:395-407
    DOI: 10.1080/10485252.2012.759219
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    Cited by:

    1. Cao, Guanqun & Wang, Li, 2018. "Simultaneous inference for the mean of repeated functional data," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 279-295.
    2. 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.
    3. Luca Macedoni & Mingzhi (Jimmy) Xu, 2022. "Flexibility And Productivity: Toward The Understanding Of Firm Heterogeneity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(3), pages 1055-1108, August.
    4. 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.
    5. 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).
    6. Zhong, Chen, 2024. "Oracle-efficient estimation and trend inference in non-stationary time series with trend and heteroscedastic ARMA error," Computational Statistics & Data Analysis, Elsevier, vol. 193(C).
    7. 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.
    8. Wang, Jiangyan & Gu, Lijie & Yang, Lijian, 2022. "Oracle-efficient estimation for functional data error distribution with simultaneous confidence band," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    9. Fuxia Cheng, 2024. "The Law of the Iterated Logarithm for L p -Norms of Kernel Estimators of Cumulative Distribution Functions," Mathematics, MDPI, vol. 12(7), pages 1-7, April.
    10. Catalina Bolancé & Carlos Alberto Acuña, 2021. "A New Kernel Estimator of Copulas Based on Beta Quantile Transformations," Mathematics, MDPI, vol. 9(10), pages 1-16, May.
    11. Jiangyan Wang & Suojin Wang & Lijian Yang, 2016. "Simultaneous confidence bands for the distribution function of a finite population and of its superpopulation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 692-709, December.
    12. 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.

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