Estimation in the partially nonlinear model by continuous optimization

Fatma Yerlikaya-Özkurt; Pakize Taylan; Müjgan Tez

doi:10.1080/02664763.2020.1864816

Estimation in the partially nonlinear model by continuous optimization

J Appl Stat. 2020 Dec 23;48(13-15):2826-2846. doi: 10.1080/02664763.2020.1864816. eCollection 2021.

Authors

Fatma Yerlikaya-Özkurt¹, Pakize Taylan², Müjgan Tez³

Affiliations

¹ Department of Industrial Engineering, Atılım University, Ankara, Turkey.
² Department of Mathematics, Dicle University, Diyarbakır, Turkey.
³ Department of Statistics, Marmara University, İstanbul, Turkey.

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.

Keywords: B-spline; Nonlinear model; continuous optimization; estimation; nonparametric regression.