INAR模型的条件最小密度功效散度估计及应用  

Conditional minimum density power divergence estimationand application for INAR models

作　　者：杨凯 孙明昱 赵志文[2] YANG Kai;SUN Ming-yu;ZHAO Zhi-wen(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China;College of Mathematics and Computer,Jilin Normal University,Siping 136000,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012 [2]吉林师范大学数学与计算机学院,吉林四平136000

出　　处：《吉林师范大学学报（自然科学版）》2024年第4期34-45,共12页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(11901053);吉林省科技发展计划项目(20220101038JC,20210101151JC)。

摘　　要：为了克服极大似然估计对异常值的敏感性,提出了一种条件最小密度功效散度估计,研究了该估计的渐近性质,包括强相合性和渐近正态性.通过数值模拟研究了该估计的估计效果.通过对季度地震数据的拟合与预测,证明了当数据集中存在异常值时,条件最小密度功效散度估计的参数估计结果比极大似然估计的结果更加准确.To overcome the sensitivity of maximum likelihood estimation to outliers,we develop a conditional version of minimum density power divergence estimator.The asymptotic property of the proposed estimator,including the strong consistency and asymptotic normality,were obtained.Some numerical simulation studies were conducted to show the performances of the conditional minimum density power divergence estimator.Finally,through the fitting and prediction of quarterly earthquake data,it was proved that the result of CMDPDE was more accurate than that of maximum likelihood estimation when there were outliers in the data set.

关 键 词：整数值时间序列 整数值自回归模型 最小密度功效散度估计 稳健估计 

分 类 号：O212.1[理学—概率论与数理统计]