更为广义的线性回归模型及其气象应用  

More generalized linear regression model and its meteorological application

作　　者：陈璇[1] 郑崇伟[1,2] 张伟涛 晋鹏 黎鑫[1] 

机构地区：[1]解放军理工大学气象海洋学院,江苏南京211101 [2]海军大连舰艇学院,辽宁大连116018 [3]解放军31110部队,江苏南京210016 [4]解放军75839部队,广东广州510510

出　　处：《解放军理工大学学报（自然科学版）》2017年第2期144-149,共6页Journal of PLA University of Science and Technology(Natural Science Edition)

基　　金：中国科学院可再生能源重点实验室开放基金资助项目(Y707k31001);中国科协高端科技创新智库青年项目(DXB-ZKQN-2016-019);山东省自然科学基金资助项目(ZR2016DL09)

摘　　要：为了解决传统的线性回归模型不具备全域分析能力以及表达能力受到模型维数限制的问题,基于要素场和矩阵的概念,提出了基于场的更为广义的线性回归模型——全回归模型。利用大规模要素场分布资料构建全回归模型,模型基本方程采用矩阵形式,方程的基本元素为要素场,相较于传统回归模型,该模型涵盖要素场整体信息。与传统回归方案进行对比分析,结果表明:该模型具有全局表达能力,在拟合过程中采用最小二乘方案可以得到全局最优结果;不同于传统回归模型的单调性特征,该模型自变量局部扰动对因变量的影响有利于分析相关过程;对于传统统计预报而言,基于矩阵分析理论及该模型全局表达能力,可以将该模型延伸应用至单站回归预报。To solve the problem that the traditional linear regression model does not have the ability for global analysis and its expression ability limited by the dimension of the regression equation,and on the basis of element fields and the matrix,a more generalized linear regression model called full regression model based on the factors with fields was proposed.Using mass elements field data,full field regression model was setup.On the basis of the matrix and elements field,this model comprehensively covers the fields＇ information and characteristics better than the traditional linear regression model.Compared to the traditional linear regression model,the results show that this model has an ability for global analysis.And on the basis of least square method,this model is global optimum in the process of fitting.In addition,different from the monotonicity features of the traditional regression model,this model has the ability of descriptive effect on the dependent variables by local perturbation of independent variables,which is conductive to the analysis of the corresponding changes by the perturbation.Otherwise,for the traditional statistical forecasting,with the global analysis ability and the matrix analysis theory,this model can be extended to a single station regression forecast.

关 键 词：全回归 要素场 统计 矩阵 

分 类 号：P731[天文地球—海洋科学]