, Volume 25, Issue 4, pp 692–709

Simultaneous confidence bands for the distribution function of a finite population and of its superpopulation

Original Paper

DOI: 10.1007/s11749-016-0491-5

Cite this article as:
Wang, J., Wang, S. & Yang, L. TEST (2016) 25: 692. doi:10.1007/s11749-016-0491-5


Simultaneous confidence bands (SCBs) are proposed for the distribution function of a finite population and of the latent superpopulation via the empirical distribution function (nonsmooth) and kernel distribution estimator (smooth) based on a simple random sample (SRS), either with or without finite population correction. It is shown that both nonsmooth and smooth SCBs achieve asymptotically the nominal confidence level under standard assumptions. In particular, the uncorrected nonsmooth SCB for superpopulation is exactly the same as the Kolmogorov–Smirnov SCB based on an independent and identically distributed sample as long as the SRS size is infinitesimal relative to the finite population size. Extensive simulation studies confirm the asymptotic properties. As an illustration, the proposed SCBs are constructed for the population distribution of the well-known baseball data (Lohr, Sampling: design and analysis, 2nd edn. Brooks/Cole, Boston, 2009).


Bandwidth Brownian bridge Kernel Kolmogorov distribution Sample survey 

Mathematics Subject Classification

62D05 62G05 62G15 62G20 

Supplementary material

11749_2016_491_MOESM1_ESM.pdf (109 kb)
Supplementary material 1 (pdf 108 KB)

Funding information

Funder NameGrant NumberFunding Note
Jiangsu Key-Discipline Program (Statistics)
  • ZY107002, ZY107992
National Natural Science Foundation of China (CN)
  • 11371272
Research Fund for the Doctoral Program of Higher Education of China
  • 20133201110002
Soochow University Excellent Doctoral Dissertation Project
  • 233200113
Jiangsu Graduate Students’ Innovative Research Project
  • KYZZ\_0331

Copyright information

© Sociedad de Estadística e Investigación Operativa 2016

Authors and Affiliations

  1. 1.Center for Advanced Statistics and Econometrics ResearchSoochow UniversitySuzhouChina
  2. 2.Department of StatisticsTexas A&M UniversityCollege StationUSA
  3. 3.Center for Statistical Science and Department of Industrial EngineeringTsinghua UniversityBeijingChina

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