Missing, Modified, and Large-p-small-n Data in Nonparametric Curve Estimation. Issue 1 (May 2017)

• Record Type: Journal Article
• Authors: Efromovich, Sam
• Is Part Of: Calcutta Statistical Association bulletin. Volume 69:Issue 1(2017:May)
• Page Start: 1
• Page End: 34
• Publication Date: 2017-05
• Subjects: Adaptation -- bias -- Big Data -- efficiency -- lower bound -- minimax -- wavelet -- AMS (2000) subject classifications: -- Primary 625G07 -- secondari 62C05 -- 62E20; Mathematical statistics -- Periodicals; Statistics -- Methodology -- Periodicals; Statistics -- Periodicals; 519.5
• DOI: 10.1177/0008068317695906
• Languages: English
• ISSNs: 0008-0683

Abstract

Nonparametric curve estimation, which makes no assumptions about shape of estimated functions, is one of the main pillars of the modern statistical science. It is used when no adequate parametric or semi-parametric model is available. Asymptotic results on adaptive estimation of nonparametric curves, under both traditional and shrinking minimaxes, are presented. The latter approach allows us to explain the phenomenon of superefficiency when a function can be estimated with a rate faster than the minimax one. Resent results on sequential nonparametric estimation, which yields an assigned risk with minimal average stopping time, are also presented. Then it is explained how the theory can be used in practically important cases of missing data, modified data in survival analysis, and Big Data. Wavelet applications in the analysis of microarrays and fMRI illustrate feasibility of the proposed nonparametric estimation.