臺灣博碩士論文加值系統

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

[1] De Gruttola, V. and Lagakos, S. (1989): Analysis of
doubly-censored survival data, with application to AIDS.
Biometrics. Vol. 45, 1-11.
[2] Finkelstein, D. M. (1986): A proportional hazard model for
interval-censored failure time data. Biometrics. Vol. 42,
845-854.
[3] Gomez, G. and Lagakos, S. W. (1994): Estimation of
the infection time and latency distribution of AIDS with doubly
censored data.
Biomertics. Vol. 50, 204-212.
[4] Lee, Chinsan (1999): An urn model in the simulation of
interval-censored failure time data. Statistics &
Probability Letters. Vol 45, 131-139.
[5] Michael P. Fay. (1999): Comparing several score tests for
interval-censored data.
Statistics in Medicine. Vol. 18, 273-285.
[6] Wei Pan (2000): A two-sample test with interval censored
data via multiple imputation. Statistics in Medicine. Vol.
19,
1-11.
[7] Sun, J. (1996): A non-parametric test for interval-censored
failure time data with application to AIDS studies.
Statistics in Medicine. Vol. 15, 1387-1395.
[8] Turnbull, B. W. (1974): Nonparamertic estimation of a
survivorship function with doubly
censored data. J. Amer. Statist. Ass. Vol. 69, 169-173.
[9] Hung-Yen Hsu (1999): The distribution of a non-parametric
test for interval failure time data. Master of science.
[10] Yu-Yu Kuo (2000): A generalization of rank tests based on
interval-censored failure time data and its application to AIDS
studies. Master of science.