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缺失数据下变系数部分非线性测量误差模型的经验似然估计

范国良1,饶诗文1,王江峰2   

  1. 1.上海海事大学经济管理学院, 上海  201306;  2.浙江工商大学统计与数学学院, 杭州 310018
  • 出版日期:2021-09-25 发布日期:2021-11-25

范国良, 饶诗文, 王江峰. 缺失数据下变系数部分非线性测量误差模型的经验似然估计[J]. 系统科学与数学, 2021, 41(9): 2643-2659.

FAN Guoliang, RAO Shiwen, WANG Jiangfeng. Empirical Likelihood Estimation for Partially Nonlinear Varying Coefficient Errors-in-Variables Models with Missing Data[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(9): 2643-2659.

Empirical Likelihood Estimation for Partially Nonlinear Varying Coefficient Errors-in-Variables Models with Missing Data

FAN Guoliang1, RAO Shiwen1 ,WANG Jiangfeng2   

  1. 1. School of Economics and Management, Shanghai Maritime University, Shanghai 201306; 2. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018
  • Online:2021-09-25 Published:2021-11-25
文章主要研究反应变量随机缺失情况下非参数部分带有测量误 差的变系数部分非线性模型中参数和非参数的经验似然估计问题.首先,基于 逆概率加权技巧,利用经验似然方法构造模型中参数和非参数部分纠偏的经 验对数似然比统计量,并在一定的条件下证明了所构造的纠偏经验对数似然 比渐近服从标准卡方分布.在此基础上可以构造参数和非参数部分的经验似 然置信域/带.模拟研究显示所提出的经验似然方法优于传统的正态逼 近方法,最后给出了一个实例研究.
In this paper, the empirical likelihood estimation of parameter and varying-coefficient function in a varying-coefficient partial nonlinear model with measurement errors in nonparametric part and missing response data. First, we apply empirical likelihood method to construct the bias-corrected empirical log-likelihood ratio statistic of parametric and nonparametric parts based on the inverse probability weighted approach. It is proved that the constructed statistics have asymptotic chi-square distribution under some mild conditions. Based on the obtained results, the empirical likelihood confidence regions of parametric and nonparametric parts can be constructed directly. Simulation results show that our proposed method outperforms the traditional normal approximation method. Finally, we give a real data analysis.
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