多元Logistic回归模型的结构变点估计  

Estimation of Structural Change in Multinomial Logistic Regression Model

作　　者：李拂晓 陈占寿[2] LI Fu-xiao;CHEN Zhan-shou(Department of Applied Mathematics,Xi'an University of Technology,Xi'an 710048,China;Department of Statistics,Qinghai Normal University,X i5ning 810000,China)

机构地区：[1]西安理工大学应用数学系,陕西西安710048 [2]青海师范大学统计系,青海西宁810000

出　　处：《数学的实践与认识》2020年第9期122-131,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11801438);陕西省自然科学基础研究计划项目(2018JQ1089);陕西教育厅科研计划项目(18JK0552)。

摘　　要：多元Logistic回归模型是广义线性模型中的一种常见形式,在社会科学和生物医学等领域有着广泛的应用.本文首先基于Pearson卡方统计量对Logistic回归模型的结构变点进行估计,再结合二元分割方法将其推广到多变点的情形.数值模拟结果表明基于Pearson卡方统计量的二元分割方法能有效估计出变点,且当变点之间间隔的样本较多时,估计效果较好.最后将此方法应用于一组DNA数据上,说明方法的有效性.Multinomial logistic regression model is a common form of generalized linear models,and is widely used in social science and biomedicine.In this paper,we first estimate the structural change based on Pearson chi-square statistic in multinomial logistic regression model,then extend the method to multiple change-point problem combined with binary segmentation procedure.Simulation results show that the binary segmentation procedure based on Pearson chi-square statistic can effectively estimate the change-points,and perform better especially when the sample size between two change-points is large.Finally,the method is applied to a DNA sequence,and the effectiveness of the proposed method is demonstrated.

关 键 词：多元Logistic回归模型 Pearson卡方统计量 二元分割法 多变点 

分 类 号：O212.1[理学—概率论与数理统计]