Rational (Padé) approximation for estimating the components of the partially-linear regression model

This paper proposes a new smoothing technique based on rational function approximation using truncated total least squares ((Formula presented.)) and compares it with the widely used smoothing spline method, which has become a very powerful smoothing technique in the semiparametric regression setting. Due to the nature of rational approximation, it generates a system of linear equations with multi-collinearities and errors in all its variables. The proposed method is mainly designed to deal with these problems, especially for solving error-contaminated systems and ill-conditioned issues. To indicate the ability of the proposed method, we perform simulation experiments under different conditions and employ a real-world data application. The outcomes from the studies show that the model parameters estimated by (Formula presented.) have lower variances than benchmarked the smoothing spline ((Formula presented.)) technique.