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

Abstract

In this paper, we propose a Pade-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 non-parametric regression setting. We consider the nonparametric regression model, y(i) = g(x(i)) + epsilon(i), and discuss how to estimate smooth regression function g where we are unsure of the underlying functional form of g. The Pade 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.