在這篇論文裡，我們證明由Fay (1999) 所提出的方法來模擬刪減區間數據經由Turnbull (1974) 的演算法來估計參數，當樣本數趨近於無窮大的時候會收斂到真正的參數。我們也提出了一種無母數的檢定方法來判斷兩母體是否來自相同的分布，模擬的結果顯示所提出的檢定統計量相當不錯

In this paper, we prove that the simulation method for
interval-censored data proposed by Fay (1999) is consistent in the
sense that if we select a sample, then the estimate obtained from
Turnbulls (1974) EM algorithm will converge to the
true parameter when the sample size tends to infinity. We also
propose a non-parametric rank test for interval-censored data to
determine whether two populations come from the same distribution.
Simulation result shows that the proposed
test statistics performs pretty satisfactory.

1. Introduction
2. Turnbulls algorithm
3. Simulation of interval-censored failure time data
3.1 Simulation with the same return probability
3.2 Simulation with different return probability
3.3 Lees selection procedure
4. Proof of consistency
4.1 Proof of consistency with the same return probability
4.2 Proof of consistency with different return probability
5. An algorithm for estimating the parameter of selected probability of admissible interval
6. A weighted rank test for
interval-censored data

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