| 罗艳虹,胡良平.适应性回归分析（Ⅰ）———回归模型的构建与求解[J].四川精神卫生杂志,2019,32(2):97-100.,Adaptive regression analysis(Ⅰ)——the construction and solution of the regression model[J].SICHUAN MENTAL HEALTH,2019,32(2):97-100 |
| 适应性回归分析（Ⅰ）———回归模型的构建与求解 |
| Adaptive regression analysis(Ⅰ)——the construction and solution of the regression model |
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| DOI：10.11886/j.issn.1007-3256.2019.02.001 |
| 中文关键词: 适应性 样条 回归分析 基函数 结点 广义交叉验证 失拟 |
| 英文关键词:Adaptability Spline Regression analysis Basis function Node Generalized cross validation Lack of fit |
| 基金项目:国家高技术研究发展计划课题资助(2015AA020102) |
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| 中文摘要: |
| 【摘要】 本文目的是介绍适应性回归模型的构建与求解方法。众所周知，在自变量数目很多时，就会出现维数灾难，此时，统计学家倾向于采用非参数回归模型取代参数回归模型。然而，当自变量数目大到一定程度时，普通的非参数回归模型也不堪重负，于是，适应性回归样条算法应运而生。此法由以下几种统计技术组成：①特殊的变量变换；②基于向前选择法构建过拟合回归模型，再基于向后选择法“ 修剪”回归模型；③基于“ 减少在向前选择的每个步骤中，检验B、V 和t的组合的数目”的基本思想，实现快速算法；④借助“GCV”和“LOF”作为“拟合优度”的界值，评价已构建的回归模型的拟合效果。此法为复杂数据结构的回归建模提供了新思路 |
| 英文摘要: |
| This paper was to introduce the construction and solution method of the adaptive regression models. As we all know, when the number of independent variables was large, the dimensional disaster would occur. At this time, statisticians tended to use a non - parametric regression model instead of a parametric regression model. However, when the number of independent variables was large to a certain extent, the usual non - parametric regression model was also overwhelmed, so the adaptive regression spline algorithm came into being. This method consisted of the following statistical techniques: ①the special variable transformations were used; ②the overfitted regression model was constructed based on the approach of forward selection, and then the regression model was" pruned" based on the approach of backward selection; ③based on the basic idea of " reducing the number of combinations of B, V and t in each step of the forward selection" , a fast algorithm was implemented; ④using " GCV" and " LOF" as the boundary value of" goodness of fit" , the fitted effect of the established regression model was evaluated. The method mentioned before provided a new way for the regression modeling of the complex data structures. |
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