均值模型中多变点问题的平均估计方法  

Model Average Estimation of Mean Model with Unknown Multiple Structural Changes

作　　者：黄淼淇 夏志明 HUANG Miaoqi;XIA Zhiming(School of Mathematics,Northwest University,Xi'an 710127)

机构地区：[1]西北大学数学学院,西安710127

出　　处：《系统科学与数学》2023年第9期2373-2387,共15页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(11771353,12171391);陕西省自然科学基础研究计划项目(2018JQ1075)资助课题。

摘　　要：文章研究了可能存在多个变点的均值突变模型的平均估计方法.给出了参数渐变的均值模型的渐近性质,说明了在模型错误设定时传统突变模型估计方法的局限性.因此文章主要通过Mallows准则建立了多变点模型的平均估计,并证明了在真实模型为变点模型的条件下,该Mallows模型平均估计量具有n1/2相合性.模拟实验结果验证了该估计量的相合性,其收敛速度为n1/2,并通过一个实例表明文章的估计方法相比于传统方法具有更高的统计效率.This paper studies the model average estimation of the mean model that may have multiple structural breaks.We give the asymptotic properties of the mean model with gradually changing parameters,which shows the limitations of the traditional estimation methods of the model with structural breaks under mis-specification.This paper mainly constructs the average estimator of the model through the Mallows'criterion,and proves that the average estimator has root-n consistency under the condition that the real model has at least one structural break.Simulation results verify the consistency of the estimator,and the convergence order is Vn.Our example shows that the estimation method in this paper has higher statistical efficiency than traditional methods.

关 键 词：均值模型 Mallows模型平均 相合性 多变点 

分 类 号：O212.1[理学—概率论与数理统计]