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利用局部加权拟合方法检验线性回归关系
引用本文:梅长林,张文修.利用局部加权拟合方法检验线性回归关系[J].系统科学与数学,2002,22(4):467-480.
作者姓名:梅长林  张文修
作者单位:1. 西安交通大学理学院,西安,710049;北京大学数学科学学院,北京,100871
2. 西安交通大学理学院,西安,710049
基金项目:国家自然科学基金(No.60075001)资助课题
摘    要:利用局部加权技术拟合变参数回归模型,提出了一个检验线性回归关系的方法.基于残差平方和,构造适当的检验统计量,给出了计算检验p-值的精确方法及三阶矩x2逼近方法.随机模拟与实例分析表明计算p-值的逼近方法具有较高的精度,所提出的检验统计量在检测回归函数非线性性方面有满意的功效和可靠性.

关 键 词:变参数回归模型  局部加权拟合  残差平方和  p-值  三阶矩x2逼近
修稿时间:2001年4月26日

TESTING LINEAR REGRESSION RELATIONSHIPS VIA LOCALLY-WEIGHTED-FITTING TECHNIQUE
Chang Lin MWI,Wen Xiu ZHANG.TESTING LINEAR REGRESSION RELATIONSHIPS VIA LOCALLY-WEIGHTED-FITTING TECHNIQUE[J].Journal of Systems Science and Mathematical Sciences,2002,22(4):467-480.
Authors:Chang Lin MWI  Wen Xiu ZHANG
Institution:(1)School of Science, Xi'an Jiaotong University, Xi'an 710049,P.R.China,School of Mathematical Sciences,Peking University, Beijing 100871,P.R.China;(2)School of Science, Xi'an Jiaotong University, Xi'an 710049,P.R.China
Abstract:This article investigates the use of locally-weighted-fitting technique to test for linearity of a regression relationship. An appropriate test statistic is constructed based on the residual sums of squares after fitting the linear and varying-parameter models. A procedure for computing the exact p-value of the test is proposed. For computational consideration in practice, a method to approximate the p-value is derived by employing the three-moment x2 approximation. Simulations and analysis of a practical problem demonstrate that the three-moment x2 approximation is rather accurate in approximating the null distribution of the statistics, and the proposed test is satisfactorily powerful in exploring non-linearity of a regression function.
Keywords:Varying-parameter regression model  locally-weighted-fitting  residual sum of squares  p-value  three-moment x2 approximation  
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