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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.Article Citation - WoS: 3Citation - Scopus: 5A Novel Comparison of Shrinkage Methods Based on Multi Criteria Decision Making in Case of Multicollinearity(American Institute of Mathematical Sciences, 2024) Kılıçoğlu,Ş.; Yerlikaya-Özkurt,F.Streszczenie. Data analysis is very important in many fields of science. The most preferred methods in data analysis is linear regression due to its simplicity to interpret and ease of application. One of the assumptions accepted while obtaining linear regression is that there is no correlation between the independent variables in the model which refers to absence of multicollinearity. As a result of multicollinearity, the variance of the parameter estimates will be high and this reduces the accuracy and reliability of the linear models. Shrinkage methods aim to handle the multicollinearity problem by minimizing the variance of the estimators in linear model. Ridge Regression, Lasso, and Elastic-Net methods are applied to different simulated data sets with different characteristics and also real world data sets. Based on performance results, the methods are compared according to multi-criteria decision making method named TOPSIS, and the order of preference is determined for each data set. © (2024), (American Institute of Mathematical Sciences). All rights reserved.
