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

Dursun Aydın, Ersin Yılmaz, Nur Chamidah

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2971-3005
Number of pages35
JournalInverse Problems in Science and Engineering
Issue number13
Publication statusPublished - 2021


  • Padé approximation
  • Partially- linear model
  • ill-posed problem
  • smoothing spline
  • truncated least squares


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