测量误差模型损失修正估计方法及其应用研究

Regression models have extensive applications in numerous fields such as economics, biomedicine, epidemiology, industrial and agricultural production, etc. However, when collecting actual data, we often cannot obtain the accurate data or all the data of variables, that is, we often encounter complex data situations such as measurement error data and missing data. In the case where there are measurement errors in the covariates of a regression model, if not corrected during parameter estimation, it is easy to produce estimation biases and reduce the estimation accuracy. In the case of missing data, if reasonable processing methods are not adopted, it will also lead to poor results of model analysis. Therefore, this paper studies the robust parameter estimation problems of linear measurement error models and partially linear measurement error models when there are measurement error data and covariates have random missing values. This paper proposes a loss-corrected estimator of parameters when the measurement error follows a Laplace distribution. Through Monte Carlo simulations and empirical analysis in medical research, it is shown that the estimation method proposed in this paper has the advantages of small bias, high accuracy, and strong robustness.

回归模型在经济学、生物医学、流行病学、工农业生产等众多领域有着广泛的应用，而我们在实际数据收集时常常无法获得变量的精确数据或全部数据，即常碰到测量误差数据、缺失数据等复杂数据情形。对于回归模型中协变量存在测量误差的情况，如在参数估计时不加以修正，易产生估计偏差，使得估计精度下降。对于数据缺失情形，如不采取合理的处理方法也会导致模型分析结果不佳。故此，本文研究了含有测量误差数据时，协变量具有随机缺失时的线性测量误差模型和部分线性测量误差模型的稳健参数估计问题。本文提出了在测量误差服从拉普拉斯分布时参数的一种损失修正估计，通过蒙特卡洛模拟和医学研究中的实证分析，显示本文所提的估计方法具有偏差小，精度高，稳健性强的优势。.