期刊文献+

基于变分法的一元非线性回归分析

Analysis of Nonlinear Regression Based on the Variational Method
下载PDF
导出
摘要 研究具有统计相关关系的二维连续型随机变量(ξ,η)的非线性回归分析问题:η=f(ξ)+ε,ξ的分布是已知的,ξ与ε独立,ε~N(0,σ2).首先推得(ξ,η)的联合密度φ(x,y),通过对φ(x,y)统计学性质、几何性质研究,将非线性回归问题归结为泛函极值问题,应用变分法,对于ξ服从不同的分布及η满足不同的约束条件,得出了依据(ξ,η)的一组样本值确定回归曲线f(x)的解析解的方法. The paper studies the analysis of two dimensional continuous random variable nonlinear regression with statistical correlation, that is, η = f(ξ) + ε , the distribution ξ is known and ξ is independent of ε, ε N(0, σ2 ) . The joint density (ξ,η) is φ(x,y) , and based on the study of the statistical properties φ(x,y) , geometrical properties, the nonlinear regression problem is considered to be attributed to functional extremum problem. By the variational method, for the different distxibutions of ξ and the dif- ferent constraint conditions of η , according to a group of sample values of (ξ, η) , the analytical method to determine the regression curvesf(x) is obtained.
作者 张同琦 李凤
出处 《渭南师范学院学报》 2012年第12期5-8,31,共5页 Journal of Weinan Normal University
基金 陕西省教育厅自然科学专项基金项目(12JK0866) 渭南师范学院科研计划项目(11YKF010)
关键词 非线性回归 样本值 变分法 泛函极值 nonlinear regression sample value variational method functional extremum
  • 相关文献

参考文献5

  • 1[美]DouglasM.Baces,[加拿大]DonaldG.Watts.非线性回归分析及应用[M].北京:中国统计出版社,1997.
  • 2书博成.非线性回归分析[M].南京:东南大学出版社,1998.
  • 3[苏]艾利斯哥尔兹.变分法[M].北京:人民教育出版社,1958.
  • 4CHEN Jin-hong. Gemai Semi parametric generalized least squares estimation in partially linear models with correlated errors [ J]. Journal of statistical planning and inference, 2007,137:117 - 132.
  • 5Huang J. Z, Shen H. P. Functional coefficient regression models for nonlinear time series: A polynomial spine approach [ J ]. Scandinavian Journal of Statistics, 2004,31 : 515 - 534.

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部