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。

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.

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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.