[1]韦博成.非线性回归模型残差的近似分析[J].东南大学学报(自然科学版),1984,14(3):115-120.[doi:10.3969/j.issn.1001-0505.1984.03.012]
 Wei Bocheng.An Approximate Residual Analysis of the Nonlinear Regression Model[J].Journal of Southeast University (Natural Science Edition),1984,14(3):115-120.[doi:10.3969/j.issn.1001-0505.1984.03.012]
点击复制

非线性回归模型残差的近似分析()
分享到:

《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
14
期数:
1984年第3期
页码:
115-120
栏目:
本刊信息
出版日期:
1984-09-20

文章信息/Info

Title:
An Approximate Residual Analysis of the Nonlinear Regression Model
作者:
韦博成
南京工学院数学力学系
Author(s):
Wei Bocheng?
Department of Mathmatics and Mechanics
关键词:
非线性回归模型 最小二乘估计 近似分析 非线性模型 残差 模型函数 线性模型理论 数学期望 曲率 列向量
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1984.03.012
摘要:
本文给出了若干近似公式,以分析非线性回归模型的最小二乘估计的残差。计算了残差的数学期望、方差和其他有关的量。所有的结果都与模型的曲率有关。如果模型为线性,则其曲率为零,我们的公式与一般线性模型理论相一致,这正是所予期的。由于我们的方法是基于二阶近似而且连系到模型的曲率,因此比一般的线性近似有较大的改进。同时,本文也给出了一个非线性模型的例子,以说明公式的应用。
Abstract:
Several approximate formulas are given for residual analysis of the least square estimator in nonlinear regression model. We investigate the expectation, variance and some releted quantities. All the results are connected with the curvature of the model. If the model is linear, then the curvature vanishes, our formulas are agree with the theory of the linear model, as expected. The formulas are preferable since they are derived from the quadratic approximation and related to the curvature of the model. An example is given to explain the results.

相似文献/References:

[1]王德育,袁春伟.TiO2薄膜厚度及其光学常数的测量[J].东南大学学报(自然科学版),1999,29(5):105.[doi:10.3969/j.issn.1001-0505.1999.05.022]
 Wang Deyu,Yuan Chunwei.Determination of the Thickness and Optical Constants of TiO2 Film[J].Journal of Southeast University (Natural Science Edition),1999,29(3):105.[doi:10.3969/j.issn.1001-0505.1999.05.022]
[2]朱仲义,李朝晖.半参数方差函数模型的核与最小二乘估计[J].东南大学学报(自然科学版),1998,28(5):148.[doi:10.3969/j.issn.1001-0505.1998.05.029]
 Zhu Zhongyi,Li Zhaohui,Li Zhaohui.The Kernel and Least Squares Estimation of Semiparametric Variance Function Model[J].Journal of Southeast University (Natural Science Edition),1998,28(3):148.[doi:10.3969/j.issn.1001-0505.1998.05.029]
[3]宋文忠,徐嗣鑫.相关—最小二乘辨识软件[J].东南大学学报(自然科学版),1981,11(3):53.[doi:10.3969/j.issn.1001-0505.1981.03.007]
 Song Wen-zhong,Xu Si-xin.Software for COR-LS Identification[J].Journal of Southeast University (Natural Science Edition),1981,11(3):53.[doi:10.3969/j.issn.1001-0505.1981.03.007]
[4]刘应安,韦博成,林金官.误差为ARMA(1,1)的非线性回归模型相关性和异方差的检验[J].东南大学学报(自然科学版),2001,31(6):98.[doi:10.3969/j.issn.1001-0505.2001.06.024]
 Liu Yingan,Wei Bocheng,Lin Jinguan.Tests of Auto-Correlation and Heteroscedasticity of the Nonlinear Regression Models with an ARMA(1,1) Sequence Random Error[J].Journal of Southeast University (Natural Science Edition),2001,31(3):98.[doi:10.3969/j.issn.1001-0505.2001.06.024]

更新日期/Last Update: 2013-05-01