進階搜尋


   電子論文尚未授權公開,紙本請查館藏目錄
(※如查詢不到或館藏狀況顯示「閉架不公開」,表示該本論文不在書庫,無法取用。)
系統識別號 U0026-3107201914160000
論文名稱(中文) 右設限資料下兩組分位數餘命函數之差的信賴帶
論文名稱(英文) Confidence bands for the difference of two quantile residual life functions with right censored data
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 107
學期 2
出版年 108
研究生(中文) 王睿廷
研究生(英文) Rui-Ting Wang
學號 R26061045
學位類別 碩士
語文別 中文
論文頁數 32頁
口試委員 指導教授-嵇允嬋
口試委員-鄭順林
口試委員-蘇佩芳
中文關鍵字 右設限資料  分位數餘命函數  信賴帶  自助重抽法 
英文關鍵字 quantile residual life function  confidence band  right censored data  bootstrap 
學科別分類
中文摘要 在右設限資料下,蔡 (2015) 博士論文中,建立Wald型式的隨機過程,並利用自助重抽法找尋臨界點,進而建構單組分位數餘命函數的信賴帶。然而,在實際例子中,常有兩組比較之情形,所以,在完整資料下,Franco-Pereira et al. (2012) 利用統計深度的概念,用自助重抽法找臨界點,建立兩組分位數餘命函數之差的信賴帶。由於Franco-Pereira et al. (2012) 所使用的方法,對於一般研究者來說過於複雜,且他們是建立在完整資料之下,而在醫學領域中,常有右設限資料。所以,本論文將用兩組樣本建立的Wald型式的隨機過程,並用兩種找臨界點的方式,建立兩組分位數餘命函數之差的信賴帶,並利用模擬的方法,探討我們提出的信賴帶的準確性。根據模擬的結果,在大樣本下,自助重抽法找到的臨界點所建立的信賴帶,較能達到預設的信心水準。
英文摘要 Quantile residual life function is widely used in many fields, such as reliability and medical studies. For right censored data, Tsai (2015) used Wald type stochastic process to construct confidence band for a quantile residual life function. Because the distribution of the supremum of the asymptotic process of Wald type stochastic process cannot be obtained analytically, so Tsai (2015) used bootstrap method to obtain the critical point to construct confidence band. For complete data, Franco-Pereira et al. (2012) used statistical depth to construct confidence band for the difference of two quantile residual life functions. Similarly, they used bootstrap method to obtain the critical point in order to construct confidence bands.

However, right censored data are collected in many medical studies. Therefore, this thesis constructs confidence band for the difference of two quantile residual life functions for right censored data. A Wald type stochastic process based on the two sample quantile residual life functions is used to construct confidence bands. Likewise, the distribution of the supremum of the asymptotic process of the Wald type stochastic process cannot be obtained analytically, so the bootstrap method is used to obtain the critical point. In addition, the method used by Parzen et al. (1997) is generalized to obtain the critical point in order to establish confidence band. The simulation study shows that the coverage rate of the confidence band which critical point obtained by bootstrap method is close to the nominal coverage rate for large sample size.
論文目次 目錄
摘要......i
英文延伸摘要......ii
目錄......vi
表目錄......viii
圖目錄......ix
第一章 緒論......1
第二章 文獻回顧......4
第一節 符號定義......4
第二節 樣本分位數餘命之推論......5
2.1 分位數餘命函數之定義......5
2.2 分位數餘命函數的點估計......6
2.3 分位數餘命的區間估計......6
2.4 樣本分位數餘命之變異數估計......8
第三節 分位數餘命函數之信賴帶......9
第四節 兩組存活函數之差的信賴帶......11
第三章 兩組分位數餘命函數的信賴帶......14
第一節 建構信賴帶的隨機過程......14
第二節 建立信賴帶所需臨界點的方法......15
2.1 自助重抽法......15
2.2 重複生成變數......16
第四章 模擬研究......19
第一節 模擬設計......19
第二節 模擬結果......23
第五章 實例分析......27
第一節 資料介紹......27
第二節 建立信賴帶......29
第六章 結論與建議......31
參考文獻......32
參考文獻 Brookmeyer, R., and Crowley, J.(1982a).“A confidence interval for the median survival time,”Biometrics, Vol. 38, No. 1, 29-41.

Chi, Y., Tsai, T. H., Tu, Y. H., and Tsai, W. Y. (2016). Comparison of several confidence intervals for median residual lifetime with left-truncated and right-censored data. Communications in Statistics-Simulation and Computation, 45(2), 701-716.

Chung, C. J. F. (1989). Confidence bands for percentile residual lifetime under random censorship model. Journal of Multivariate Analysis, 29(1), 94-126

Csörgő, S., and Viharos, L. (1992). Confidence bands for percentile residual lifetime.
Journal of statistical planning and inference, 30(3), 327-337

Fleming, T. R., and Harrington, D. P. (1991). Counting processes and survival analysis. John Wiley & Sons.

Franco-Pereira, A. M., Lillo R. E. and Romo J. (2012). Comparing quantile residual life functions by confidence bands. Lifetime Data Analysis 18, 195–214.

Jeong, J. H., Jung, S. H. and Costantino, J. P. (2008). Nonparametric inference on median residual life function. Biometrics, 64, 157-163

Kaplan, E. L., and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American statistical association, 53(282), 457-481.

Parzen, M. I., Wei, L. J., and Ying, Z. (1997). Simultaneous confidence intervals for the difference of two survival functions. Scandinavian Journal of Statistics,24(3), 309-314

Tsai, T. H., Tsai, W. Y., Chi, Y. C. and Chang, S. M. (2016). Estimation of the ratio of two median residual lifetimes with left-truncated and right-censored data. Biometrics.

Zhou, M. and Jeong, J. H. (2011). Empirical likelihood ratio test for median and mean residual lifetime. Statistics in Medicine 30, 152-159

蔡承憲 (2015), 左截斷右設限資料下分位數餘命函數之信賴帶. 國立成功大學統計學系博士論文.
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2024-08-01起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2024-08-01起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw