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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 江金倉(Chin-Tsang Chiang) | |
dc.contributor.author | Shao-Hsuan Wang | en |
dc.contributor.author | 王紹宣 | zh_TW |
dc.date.accessioned | 2021-06-12T18:11:15Z | - |
dc.date.available | 2008-11-15 | |
dc.date.copyright | 2007-11-15 | |
dc.date.issued | 2007 | |
dc.date.submitted | 2007-10-11 | |
dc.identifier.citation | 1. Bickel, P. J., G‥otze, F., and Van Zwet, W. R. (1986). The Edgeworth
expansion for U-statistics of degree 2. The Annals of Statistics. 19, 470-484. 2. Callaert, H., Janssen, P., and Veraverbeke, N. (1980). An edgeworth expansion for U-statistics. The Annals of Statistics. 8, 299-312. 3. Callaert, H. and Veraverbeke, N. (1981). The order of the Normal approximation for a studentized U-statistic. The Annals of Statistics. 9, 194-200. 4. Chambless, L. E. and Diao, G. (2006). Estimation of time-dependent area under the ROC curve for long-term risk prediction. Statistics in Medicine. 25, 3474-3486. 5. Chang, M. N. and Rao, P. V. (1989). Berry-Esseen bound for the Kaplan-Meier estimator. Communication in Statistics-Theory and Methods. 18, 4647-4664. 6. Chang, M. N. (1991). Edgeworth expansion for the Kaplan-Meier estimator. Communication in Statistics-Theory and Methods. 20, 2479- 2494. 7. Chiang, C. T., James, L. F., and Wang, M. C. (2005). Random weighted bootstrap method for recurrent events with informative censoring. Lifetime Data Analysis. 11, 489-509. 8. Cornish, E. A. and Fisher, R. A. (1937). Moments and cumulants in the specification of distributions. Review of the International Statistical Institute. 5, 307-320. 9. Fleming, T. R. and Harrington, D. P. (1991). Counting process and survival analysis. New York:Wiley. 10. Helmers, R. (1991). On the Edgeworth expansion and the Bootstrap approximation for a studentized U-statistic. The Annals of Statistics. 19, 470-484. 11. Hung, H and Chiang, C. T. (2007). Estimation methods for timedependent AUC models with survival data. Technical Report. 12. Janssen, P. (1994). Weighted bootstrapping of U-statistics. Journal of Statistical Planning and Inference. 38, 31-42. 13. Kalbfleisch, J. D. and Prentice, R. L. (2002). The Statistical Analysis of Failure Time Data. New York:Wiley. 14. Malevich, T. L. and Abdalimov, B. (1979). Large deviation probabilities for U-statistics. Theory of Probability and its Applications. 24, 215-219. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27594 | - |
dc.description.abstract | 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。 | zh_TW |
dc.description.abstract | 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. | en |
dc.description.provenance | Made available in DSpace on 2021-06-12T18:11:15Z (GMT). No. of bitstreams: 1 ntu-96-R93221024-1.pdf: 252881 bytes, checksum: 61433bf251e4629dd593fd0435f2b245 (MD5) Previous issue date: 2007 | en |
dc.description.tableofcontents | 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 ...... 32 | |
dc.language.iso | en | |
dc.title | 時間相關之AUC統計推論 - 加權自助法與Edgeworth展式 | zh_TW |
dc.title | Weighted Bootstrap and Edgeworth
Expansion for the Nonparametric Estimator of Time-Dependent AUC | en |
dc.type | Thesis | |
dc.date.schoolyear | 96-1 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 陳宏(Hung Chen),張子貴(Tzu-Kui Chang) | |
dc.subject.keyword | AUC,Edgeworth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, | zh_TW |
dc.subject.keyword | AUC,Edgeworth expansion,Kaplan-Meier estimator,normal approximation,random weighted, | en |
dc.relation.page | 35 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2007-10-11 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
顯示於系所單位: | 數學系 |
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