Confidence and prediction intervals based on interpolated records. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Ahmadi, Jafar; Basiri, Elham; Kundu, Debasis
• Is Part Of: Journal of nonparametric statistics. Volume 29:Issue 1(2017)
• Page Start: 1
• Page End: 21
• Publication Date: 2017-01-02
• Subjects: Interpolated records -- quantile -- coverage probability -- coverage error; 62G15 -- 62G30; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2016.1239826
• Languages: English
• ISSNs: 1048-5252

Abstract

ABSTRACT: In several statistical problems, nonparametric confidence intervals for population quantiles can be constructed and their coverage probabilities can be computed exactly, but cannot in general be rendered equal to a pre-determined level. The same difficulty arises for coverage probabilities of nonparametric prediction intervals for future observations. One solution to this difficulty is to interpolate between intervals which have the closest coverage probability from above and below to the pre-determined level. In this paper, confidence intervals for population quantiles are constructed based on interpolated upper and lower records. Subsequently, prediction intervals are obtained for future upper records based on interpolated upper records. Additionally, we derive upper bounds for the coverage error of these confidence and prediction intervals. Finally, our results are applied to some real data sets. Also, a comparison via a simulation study is done with similar classical intervals obtained before.