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Article Citation - WoS: 2Citation - Scopus: 2Estimation in the Partially Nonlinear Model by Continuous Optimization(Taylor & Francis Ltd, 2021) Yerlikaya-Ozkurt, Fatma; Taylan, Pakize; Tez, MujganA 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.Article Citation - WoS: 1Citation - Scopus: 1Spline Based Sparseness and Smoothness for Partially Nonlinear Model Via C-Fused Lasso(American Institute of Mathematical Sciences, 2025) Taylan, P.; Yerlikaya-¨Ozkurt, F.; Tez, M.One of the most beneficial and widely used models for data analysis are partially nonlinear models (PNLRM), which consists of parametric and nonparametric components. Since the model includes the coefficients of both the parametric and nonparametric parts, the complexity of the model will be high and its interpretation will be very difficult. In this study, we propose a procedure that not only achieves sparseness, but also smoothness for PNLRM to obtain a simpler model that better explains the relationship between the response and covariates. Thus, the fused Lasso problem is taken into account where nonparametric components are expressed as a spline basis function, and then the Fused Lasso estimation problem is built and expressed in terms of conic quadratic programming. Applications are conducted to evaluate the performance of the proposed method by considering commonly utilized measures. Promising results are obtained, especially in the data with nonlinearly correlated variables. © (2025), (American Institute of Mathematical Sciences). All rights reserved.
