在雙截斷資料下，因為存活函數是無法被唯一估計，但在給定範圍下的條件存活函數是可被估計的。於是，Tsai和Zhang (1995) 在雙截斷資料下，探討條件存活函數之無母數最大概似估計量之漸近性質，Efron與Petrosian (1999) 則提供自我一致的方式估計條件存活函數，其方法能較清楚了解雙截斷資料對存活函數估計的影響。此外，嵇等 (2004) 則提供雙截斷資料下，兩組條件存活函數的檢定方法，Shen (2010) 採用半參數方式比較兩組條件存活函數。另外，針對左截斷與右設限資料，Hung (2012) 提供檢定兩組平均餘命之方法。然而，截至目前為止尚未有學者專家提供雙截斷資料下，比較兩組平均餘命的方法。相同地，在雙截斷資料下，平均餘命亦無法估計，故本論文依據條件存活函數定義條件平均餘命。接著，本論文中將以自我一致估計式估計條件平均餘命，並建構一檢定統計量比較兩組的條件平均餘命。模擬驗證了所建議的檢定統計量之漸近抽樣分布為標準常態分布。另外，應用Berger et al. (1988)交集-聯集檢定法(intersection-union test) 進一步找出在哪些時間點上，兩組之條件平均餘命有所差異。最後，以本論文所提的檢定方法來比較相同建材下，台灣不同地區建築物使用年限在觀察範圍內的條件平均餘命。

Recently, several methods have been proposed to estimate the survival function based on doubly truncated data. For example, Tsai and Zhang (1995) derived some asymptotic properties of the nonparametric maximum likelihood estimator of conditional survival function for doubly truncated data, while Efron and Petrosian (1999) derived a self-consistent algorithm for estimating conditional survival function. Moreover, Chi et al. (2004) proposed two test statistics to test the equality of two survival functions with doubly truncated data, whereas Shen (2010) suggested a semi-parametric test for the comparison of two survival functions. In addition, Hung (2012) proposed a test statistic to test the equality of two mean residual life functions with left truncated and right censored data. However, nonparametric methods for comparing two mean residual life functions have not been developed for doubly truncated data. Therefore, this paper proposes a test statistic based on the differences between two estimated conditional mean residual life functions to compare two conditional mean residual life functions with doubly truncated data. Moreover, the intersection-union test, proposed by Berger et al. (1988), is used to construct confidence set which specified a range of values for one conditional mean residual life function dominates the other. The comparative results from a simulation study are presented and the implementation of the proposed method to one real data set is illustrated.

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