分段线性模型误差分布差异的经验似然比检验  

Empirical Likelihood Ratio Test for the Differences of Errors Distribution in Piecewise Linear Models

作　　者：高鹏丽 夏志明 GAO Pengli;XIA Zhiming(School of Mathematics,Northwest University,Xi’an 710127,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《山西大学学报（自然科学版）》2020年第1期30-37,共8页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11771353)。

摘　　要：为了明确分段线性模型的误差之间是否存在分段差异,文章基于残差中的经验似然思想建立了假设检验方法。首先,基于真实误差构造经验似然函数,求出其渐近分布。然后,基于残差构造经验似然比统计量,并给出了原假设成立时统计量的渐近分布。最后进行Monte Carlo模拟,验证理论的正确性;结果表明,当样本量较大时,在原假设下,基于残差构造的统计量的渐近分布具有很好的表现。In order to clarify whether there are piecewise differences between the errors in the piecewise linear model,this paper established a hypothesis test method based on the empirical likelihood of residuals.First,the empirical likelihood function was constructed based on real errors and its asymptotic distribution was obtained.Secend,the empirical likelihood ratio statistics was constructed based on residuals,and the asymptotic distribution of statistics was given when the null hypothesis was established.Finally,Monte Carlo simulation was carried out to verify the correctness of the theory.The results showed that the asymptotic distribution of the statistics constructed based on residuals performed well under the null hypothesis when the sample size was large.

关 键 词：分段线性模型 残差 经验似然比检验 MONTE CARLO模拟 

分 类 号：O212.1[理学—概率论与数理统计]