Convergence Rates of Multivariate Regression Estimators with Errors-In-Variables. (2nd December 2017)

• Record Type: Journal Article
• Authors: Guo, Huijun; Liu, Youming
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 12(2017)
• Page Start: 1564
• Page End: 1588
• Publication Date: 2017-12-02
• Subjects: Convergence rate -- Fourier-oscillating -- optimality -- noise -- regression function; 62G07 -- 62G20 -- 42C40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1349145
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: This paper studies the regression estimation with errors-in-variables. We first extend Meister's theorems (Meister, 2009. Deconvolution Problems in Nonparametric Statistics . Springer, Berlin) from one to multi-dimensional setting, when a noise density has no zeros in the Fourier domain. Then motivated by the work of Delaigle and Meister (Delaigle, Meister, 2011. Nonparametric function estimation under Fourier-oscillating noise. Statistica Sinica 21, 1065–1092), we show a desired convergence rate of a kernel estimator for Fourier-oscillating noises. Finally, two technical conditions are removed, when a wavelet estimator is used.