TEST

, Volume 25, Issue 4, pp 692–709 | Cite as

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

Original Paper

Abstract

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).

Keywords

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)

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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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