Estimation in the Partially Nonlinear Model by Continuous Optimization

Abstract

A useful model for data analysis is the partially nonlinear model where response variable is represented as the sum of a nonparametric and a parametric component. In this study, we propose a new procedure for estimating the parameters in the partially nonlinear models. Therefore, we consider penalized profile nonlinear least square problem where nonparametric components are expressed as a B-spline basis function, and then estimation problem is expressed in terms of conic quadratic programming which is a continuous optimization problem and solved interior point method. An application study is conducted to evaluate the performance of the proposed method by considering some well-known performance measures. The results are compared against parametric nonlinear model.