江金倉臺灣大學：數學研究所王紹宣Wang, Shao-HsuanShao-HsuanWang2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/59405根據非參數AUC 估計式之常態逼近理論所得之信賴區間已被建立。然而, 當樣本數 過小及設限率偏高時, 所建立之信賴區間顯現涵蓋機率過低及區間不精確問題。為了 解決此缺點, 吾等利用加權自助法和Edgeworth 展式方法來改進涵蓋率和區間分位 的精確性。在此論文, 針對加權自助分配和Edegeworth 展式作深入理論建立, 並在 一系列的數值模擬中歸納出不同方法之性質。最後, 將所提出之方法應用於ACTG 175 研究資料上。The confidence region for the time-dependent area under the receiver operating characteristic curve (AUC) has been constructed based on the asymptotic normality of a non-parametric estimator. However, the performance of the normal approximated confidence interval is very poor when the sample size is small and the censoring rate is high. To improve the coverage probability and the accuracy of confidence interval, the random weighted bootstrap distribution and the Edgeworth expansion with remainder term o(n^(?1/2)) are proposed to approximate the sampling distribution of the estimator. The asymptotic properties of the random weighted bootstrap approximation and the Edgeworth expansion are studied in this thesis. The usefulness of the proposed procedures are confirmed by a class of simulations with different sample sizes and censoring rates. Moreover, the methods are demonstrated using the ACTG 175 data.1. Chapter 1 Introduction .....1 2. Chapter 2 Estimation of θt .....4 3. Chapter 3 Random Weighted Bootstrap .....7 4. Chapter 4 Edgeworth Expansion .....13 5. Chapter 5 Simulation Study .....23 6. Chapter 6 Application to ACTG 175 Data .....30 7. Chapter 7 Concluding Remarks ...... 32252881 bytesapplication/pdfen-USAUCEdgeworth展式kaplan-meier估計式常態逼近理論存活資料加權自助法U統計量Edgeworth expansionKaplan-Meier estimatornormal approximationrandom weightedthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59405/1/ntu-96-R93221024-1.pdf