Estimating the Nonparametric Regression Function by Using Padé Approximation Based on Total Least Squares

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, 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.