Resumen de Simultaneous confidence bands for the distribution function of a finite population and of its superpopulation
Jiangyan Wang, Suojin Wang, Lijian Yang
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).
