在本論文中，我們考慮兩個統計模型：(i) 計數資料的零截段模型與 (ii) 結合 Cox 的風險比例模型 (proportional hazards model) 與隨機效應模型的聯合建模 (joint modeling) 之模型。在這兩個模型中，有差別性測量誤差的問題會自然產生。針對這個問題，我們提出誤差增量 (error augmentation) 估計方法，此方法除了能解決有差別性測量誤差的問題外，也可以提高原先估計方法的效率。 In the context of measurement error problems, most of the literatures assumed that the measurement error is nondifferential, that is, the measurement error is independent to the response variable. In other words, measurement error contains no information for the response variable. Such assumption may be plausible for many applications in practice. Nevertheless, there are occasions that number of repeat measurements depends on the response variable and hence the accuracy of averaged surrogate depends on the response variable, too. This situation induces a differential measurement error problem and there was no satisfactory analysis for the problem so far in general.
In this thesis, we consider two regression models: (i) a zero-value truncated model for count data and (ii) a joint modeling for the Cox proportional hazards model and a random effect model. The differential measurement error problems arise naturally in these two models. In this thesis, we propose the error augmentation method. It could not only solve the problem brought by differential measurement errors, but also enhance the efficiency of the original estimating method.
