Bootstrap Confidence Intervals for Large-scale Multivariate Monotonic Regression Problems. Issue 3 (15th March 2016)

• Record Type: Journal Article
• Authors: Sysoev, Oleg; Grimvall, Anders; Burdakov, Oleg
• Is Part Of: Communications in statistics. Volume 45:Issue 3(2016)
• Page Start: 1025
• Page End: 1040
• Publication Date: 2016-03-15
• Subjects: Big data -- Bootstrap -- Confidence intervals -- Monotonic regression -- Pool-adjacent-violators algorithm.; 62G08; 62G09.; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2014.911899
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract : Recently, the methods used to estimate monotonic regression (MR) models have been substantially improved, and some algorithms can now produce high-accuracy monotonic fits to multivariate datasets containing over a million observations. Nevertheless, the computational burden can be prohibitively large for resampling techniques in which numerous datasets are processed independently of each other. Here, we present efficient algorithms for estimation of confidence limits in large-scale settings that take into account the similarity of the bootstrap or jackknifed datasets to which MR models are fitted. In addition, we introduce modifications that substantially improve the accuracy of MR solutions for binary response variables. The performance of our algorithms is illustrated using data on death in coronary heart disease for a large population. This example also illustrates that MR can be a valuable complement to logistic regression.