Truncation level selection in nonparametric regression using Padé approximation

Abstract

This paper introduces a Padé-type approximation for an unknown regression function in a nonparametric regression model. This newly introduced approximation provides a linear model with multi-collinearities and errors in all its variables. To deal with these issues, we used the truncated total least squares (TTLS) method. The efficient implementation of a Padé-type method using TTLS depends on choosing a truncation level. To provide an optimum truncation level for this method, we update the conventional parameter selection methods, including the generalized cross validation (GCV), improved version of the Akaike information criterion (AICc), restricted maximum likelihood (REML), Bayesian information criterion (BIC), and Mallows’ C_p criterion. The primary aim of this study is to compare the performances of these level selection methods. A Monte Carlo simulation and a real data example are performed to illustrate the ideas in the paper. The results confirm that the GCV and AICc slightly outperform the other methods, especially when sample sizes are small and large, respectively.

Keywords:

• Truncation level
• Selection methods
• Total least squares
• Regression function