Bootstrapping Conic Multivariate Adaptive Regression Splines (Bcmars)
نویسندگان
چکیده
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). CMARS is the modified version of the well-known nonparametric regression model, Multivariate Adaptive Regression Splines (MARS), which uses conic quadratic optimization (CQP). CMARS is at least as complex as MARS even though 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 efficiency. The results imply that Random-X method produces more precise, accurate and less complex models for medium size and medium scale data.
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