关键词: 测量误差模型, 损失修正, 缺失数据, 稳健估计

Abstract: Regression models have been widely used in many fields, such as economics, biology, medicine, epidemiology, industrial and agricultural production, etc. However, for various reasons, in the process of data collection, data inaccuracy is inevitable. We often encounter data with errors of measurement, missing data, and other complicated data issues. In the presence of measurement errors in regression models, if we donot correct the parameter estimation method, it is easy to produce estimation deviation and lead to the decrease of estimation accuracy. For missing data, if we do not take a reasonable treatment method, the analysis results a model will be less satisfactory. Therefore, this paper studies the partial linear errors-in- variables model and the linear errors-in-variables model with covariate data missing at random. A loss correction method of parameter estimation is proposed, when the measurement error follows the Laplace distribution. With Monte Carlo simulation and real data analysis in medical research, the results show that the proposed method has the advantages of small deviation, high accuracy and strong robustness.

Key words: Errors-in-variables Model, Loss Correction, Missing Data, Robustness