A well-defined model can relate phenomena and conclusions, which can enhance our understanding of knowledge and help our work decisively. In statistics, one popular research topic is to formulate mathematical models using existing data. Many methods have been proposed, such as multivariate adaptive regression splines (MARS), multiple linear regression (MLR), and conic multivariate adaptive regression splines (CMARS).

MARS is a nonparametric regression method that builds a model in two rounds. CMARS is an improved version of MARS using conic quadratic programming. Bootstrap is a resampling technique that can work with a wide range of models, which estimates the sampling distribution and the significance of parameters in a model. MARS has proved to be powerful for handling high-dimensional and voluminous data, while CMARS is more accurate and robust. However, models produced by the CMARS method are more complex.

In this paper, the authors try to reduce the complexity of models from CMARS. A bootstrapping CMARS (BCMARS) method is proposed, which is a combination of bootstrapping methods and CMARS. Three bootstrapping methods are studied, including residual bootstrap (fixed-X resampling), pairs bootstrap (random-X resampling), and wild bootstrap. Four datasets are used to “compare the performances of models developed by using MARS, CMARS, and BCMARS”; “accuracy, precision, stability, efficiency, and robustness are considered.” The results show that the bootstrapping CMARS method with random-X resampling is the best-performing method.

The method developed in this paper produces “more accurate, precise, and less complex models.” This method will be useful in real-world applications and for researchers who work on related topics.