Estimating the Nonparametric Regression Function by Using Padé Approximation Based on Total Least Squares. (18th August 2020)

• Record Type: Journal Article
• Authors: Ahmed, Syed Ejaz; Aydin, Dursun; Yilmaz, Ersin
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 15(2020)
• Page Start: 1827
• Page End: 1870
• Publication Date: 2020-08-18
• Subjects: Alternative smoothing method -- nonparametric regression -- Padé approximation -- splines -- truncated total least squares; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1794891
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we propose a Padé-type approximation based on truncated total least squares ( P – TTLS ) and compare it with three commonly used smoothing methods: Penalized spline, Kernel smoothing and smoothing spline methods that have become very powerful smoothing techniques in the nonparametric regression setting. We consider the nonparametric regression model, y i = g ( x i ) + ε i, and discuss how to estimate smooth regression function g where we are unsure of the underlying functional form of g . The Padé approximation provides a linear model with multi-collinearities and errors in all its variables. The P – TTLS method is primarily designed to address these issues, especially for solving error-contaminated systems and ill-conditioned problems. To demonstrate the ability of the method, we conduct Monte Carlo simulations under different conditions and employ a real data example. The outcomes of the experiments show that the fitted curve solved by P – TTLS is superior to and more stable than the benchmarked penalized spline ( B – PS ), Kernel smoothing ( KS ) and smoothing spline ( SS ) techniques.