caa a22 4500 605477906 CHVBK 20210128100403.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10994-015-5502-3 doi (NATIONALLICENCE)springer-10.1007/s10994-015-5502-3 A computational approach to nonparametric regression: bootstrapping CMARS method [Elektronische Daten] [Ceyda Yazıcı, Fatma Yerlikaya-Özkurt, İnci Batmaz] Bootstrapping is a computer-intensive statistical method which treats the data set as a population and draws samples from it with replacement. This resampling method has wide application areas especially in mathematically intractable problems. In this study, it is used to obtain the empirical distributions of the parameters to determine whether they are statistically significant or not in a special case of nonparametric regression, conic multivariate adaptive regression splines (CMARS), a statistical machine learning algorithm. CMARS is the modified version of the well-known nonparametric regression model, multivariate adaptive regression splines (MARS), which uses conic quadratic optimization. CMARS is at least as complex as MARS even though it performs better with respect to several criteria. To achieve a better performance of CMARS with a less complex model, three different bootstrapping regression methods, namely, random-X, fixed-X and wild bootstrap are applied on four data sets with different size and scale. Then, the performances of the models are compared using various criteria including accuracy, precision, complexity, stability, robustness and computational efficiency. The results imply that bootstrap methods give more precise parameter estimates although they are computationally inefficient and that among all, random-X resampling produces better models, particularly for medium size and scale data sets. The Author(s), 2015 Bootstrapping regression nationallicence Conic multivariate adaptive regression splines nationallicence Fixed-X resampling nationallicence Random-X resampling nationallicence Wild bootstrap nationallicence Machine learning nationallicence Yazıcı Ceyda Department of Statistics, Middle East Technical University, Ankara, Turkey aut Yerlikaya-Özkurt Fatma Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey aut Batmaz İnci Department of Statistics, Middle East Technical University, Ankara, Turkey aut Machine Learning Springer US; http://www.springer-ny.com 101/1-3(2015-10-01), 211-230 0885-6125 101:1-3<211 2015 101 10994 https://doi.org/10.1007/s10994-015-5502-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10994-015-5502-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yazıcı Ceyda Department of Statistics, Middle East Technical University, Ankara, Turkey aut NATIONALLICENCE 700 1- Yerlikaya-Özkurt Fatma Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey aut NATIONALLICENCE 700 1- Batmaz İnci Department of Statistics, Middle East Technical University, Ankara, Turkey aut NATIONALLICENCE 773 0- Machine Learning Springer US; http://www.springer-ny.com 101/1-3(2015-10-01), 211-230 0885-6125 101:1-3<211 2015 101 10994