條件眾數的分位數回歸估計法(Quantile Regression approach to conditional Mode estimation/QRM)是近年來提出的一種在給定回歸變量的情况下估計結果變量條件眾數的方法。然而，在對真實數據進行分析時，我們往往需要處理受限資料。由於QRM沒有考慮受限資料，所以可能會給出高度偏差的估計。因此本文延用QRM的做法，用受限資料條件分位數估計法(the method of estimate conditional quantile regression for censored data /QRC)取代了QRM中使用的傳統條件分位數估計法(traditional estimation approach of conditional quantile regression /QR)，稱為受限資料條件眾數的分位數回歸估計方法(Quantile Regression for censored data approach to conditional Mode estimation /QRM-C)。
然而與QR比較之下，QRC的計算時間更長。QRM中提到的估計值是通過最小化估計導數得到的，它在計算上很具吸引力，而估計導數的最小化是一個一維優化問題，因此可以通過網格搜尋來實現。由於QRM在網格搜索的過程中都需要重複QR多次，所以在我們的方法中用QRC代替QR時，計算耗時較長。所以我們用夾擠搜尋法代替了網格搜索。相比QRM，QRM-C估計量在處理受限資料時更為準確、偏差更小。此外，QRM-C搭配夾擠搜尋法的計算時間比QRM-C搭配網格搜索更短。我們還將我們的方法應用於科羅拉多高原鈾礦工人隊列數據，並與QRM進行比較。模擬實驗和實際數據應用發現，QRM-C在受限資料處理中具有良好的估計結果並且可以通過改變尋找函数導數最低點的方法來縮短運算時間。

Quantile Regression approach to conditional Mode estimation(QRM) is a method of estimating the conditional mode of an outcome variable for given regressors. However, we often need to deal with censored data in the regression analysis of real data. And this approach may give highly biased estimates for censored data. So we followed the method of QRM and replaced the traditional estimation approach of conditional quantile regression(QR) with the method of estimating conditional quantile regression for censored data(QRC) in this thesis. We called this method Quantile Regression approach to conditional Mode estimation for Censored data(QRM-C).
However, compared to QR, QRC required longer computing time. In QRM, the proposed estimator is obtained by minimizing the estimated derivative, and is computationally attractive because the minimization of the estimated derivative is a one-dimensional optimization problem and so can be carried out by a grid search. Since QRM needs to apply QR algorithm many times for each procedure of grid search, our method will also take a long computing time when we substituted the QRC for QR directly. So we replaced the grid search with squeeze method instead. Comparing with QRM, the estimator of QRM-C is more accurate and has smaller bias when dealing with censored data. In addition, the computing time of QRM-C with squeeze search is shorter than the computing time of QRM-C with grid search. We also apply our method to the Colorado Plateau uranium miners cohort data and compare the performance with QRM. The simulation results and real data application show that QRM-C has good performance in censored data and the operation time can be shortened by changing the method of finding the minimum position of the derivative of function.

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