Simultaneous Confidence Bands for the Distribution Function of a Finite Population

• Activity Number: 92
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 9:30 PM to 10:15 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jiangyan Wang* and Suojin Wang and Lijian Yang
• Companies: Soochow University and Texas A&M University and Soochow University
• Keywords: Bandwidth ; Kernel ; Kolmogorov distribution ; Sample survey ; Superpopulation

Abstract

Simultaneous confidence bands (SCBs) are proposed for the distribution function of a finite population and superpopulation via the empirical distribution function (nonsmooth) and kernel distribution estimator (KDE, 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 iid sample as long as the SRS size is infinitesimal relative to the finite population size. Extensive simulation studies confirm the asymptotic properties. The proposed SCBs are constructed for the population distribution of the well-known Baseball data (Lohr 2009) from large number of SRSs, and the findings confirm the theoretical results.