Data sharpening on unknown manifold. Issue 23 (2nd December 2017)

• Record Type: Journal Article
• Authors: Kudo, Masaki; Naito, Kanta
• Is Part Of: Communications in statistics. Volume 46:Issue 23(2017)
• Page Start: 11721
• Page End: 11744
• Publication Date: 2017-12-02
• Subjects: Bias reduction -- Data sharpening -- Manifold -- Non parametric regression; 62G08; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2016.1277756
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: This article is concerned with data sharpening (DS) technique in nonparametric regression under the setting where the multivariate predictor is embedded in an unknown low-dimensional manifold. Theoretical asymptotic bias is derived, which reveals that the proposed DS estimator has a reduced bias compared to the usual local linear estimator. The asymptotic normality of the DS estimator is also developed. It can be confirmed from simulation and applications to real data that the bias reduction for the DS estimator supported on unknown manifold is evident.