doi:  10.3878/j.issn.1006-9895.1808.18108
一种新的线性回归模型及其应用示例

A new linear regression model and its application
摘要点击 207  全文点击 61  投稿时间:2018-01-15  修订日期:2018-07-10
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基金:  高端科技创新智库青年项目(No. DXB-ZKQN-2016-019);国家重点基础研究发展规划项目(2013CB956200);中国科学院可再生能源重点实验室开放基金(No. Y707k31001).
中文关键词:  线性回归  统计  更为广义
英文关键词:  regression  statistics  more generalized
              
作者中文名作者英文名单位
陈璇chenxuan解放军75839部队
游小宝YOU Xiaobao北京应用气象研究所
郑崇伟ZHENG Chongwei海军大连舰艇学院
孙威SUN Wei陆军工程大学
谢胜浪XIE Shenglang解放军95080部队
引用:陈璇,游小宝,郑崇伟,孙威,谢胜浪.2019.一种新的线性回归模型及其应用示例[J].大气科学
Citation:chenxuan,YOU Xiaobao,ZHENG Chongwei,SUN Wei,XIE Shenglang.2019.A new linear regression model and its application[J].Chinese Journal of Atmospheric Sciences (in Chinese)
中文摘要:
      回归分析是统计分析中常用手段之一,传统的回归模型不具备全域分析能力,而变量场之间的关系多采用SVD等方案进行分析,与传统的回归分析有所脱节。更为广义的线性回归模型是传统线性回归模型的延拓,在标量情况下,该模型可转化为传统线性回归模型,其基本特征包含乘法不可互易性、等价于传统线性回归、可分析性、延拓性、降维特征及容错性等。该模型解决了传统的线性回归模型不具备全域分析能力及模型表达能力受限于模型维数的现实问题。本文采用了NCEP降水、高度场、风场月平均资料及国家气候中心西太副高指数资料,利用该模型和传统回归方案进行对比分析,分析结果表明,该模型具有一定的实用参考价值。
Abstract:
      Regression analysis is one of the common methods in statistical analysis. The traditional regression model does not have the ability of global analysis and the relationship between the variables fields is analyzed by these methods such as SVD, which cause the disconnection with the traditional regression analysis. The more generalized linear regression model is the extension of traditional linear regression model, in the case of scalar, the model can be transformed into a traditional linear regression model, and its basic features include non-commutative multiplication, equivalent to traditional linear regression, analysis, extension, dimensionality reduction and robustness, etc. This model solves the status that the traditional linear regression model does not have global analysis ability and the expression ability of the model is limited by the dimension of the regression equation. In this paper, the monthly average data of precipitation, height field and wind field from NCEP and the Western Pacific subtropical high index data from the National Climate Center are adopted, on the basis of this model, with the traditional regression as compared model, the results show that the more generalized linear regression model has practical value and reference value.
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