题目：Robust Estimation for Longitudinal Data with Covariate Measurement Errors and Outliers
Measurement errors and outliers often arise in longitudinal data, ignoring the effects of measurement errors and outliers will lead to seriously biased estimators. Therefore, it is important to take them into account in longitudinal data analysis. In this paper, we develop a robust estimating equation method for analysis of longitudinal data with covariate measurement errors and outliers. Specifically, we eliminate the effects of measurement errors by making use of the independence of replicate measurement errors and correct the bias induced by outliers through centralizing the matrix of error-prone covariates in the estimating equation. The proposed method is easy to implement by using the standard generalized estimating equations algorithms and does not require specifying the distributions of the true covariates, response and measurement error. The asymptotic normality of the proposed estimator is established under some regularity conditions. Extensive simulation studies show that the proposed method does have a good performance in handling measurement errors and outliers. In the end, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition (LEAN) study for illustration.
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