Simultaneous confidence bands (SCBs) are proposed for the distribution
function of a finite population and of the latent superpopulation via the empirical dis-
tribution 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 infini-
tesimal 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).

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