# 臺灣博碩士論文加值系統

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 這篇文章中基於單一檢測時間之二元現時狀態數據，提供一種無母數檢定方法，檢定其邊際存活函數是否獨立。有別於使用無母數最大概似估計法收斂速率為n^(1/3)之邊際存活函數估計，在此考慮Sieve估計量以得到任意收斂速率的邊際存活函數估計。文中除了提供建構之檢定統計量之大樣本推論，亦透過統計模擬探討有限樣本下該檢定統計量的可行性．由模擬結果發現，邊際存活函數之估計量在收斂速率在n^(3/8)時檢定力最大。
 This article develops a nonparametric procedure for testing marginal independence based on bivariate current status data with common monitoring time. Instead of using nonparametric maximum likelihood technique to estimate the marginal survival function, the Sieve estimator technique is applied so that not only the convergence rate of the marginal survival function at n^(1/3) be considered. Asymptotic properties of the proposed tests are derived, and their finite sample performance is studied via simulation. The simulation results show that the test statistic with convergence rate of the marginal survival function at n^(3/8) gives the most power in almost all the cases and have larger power than all the recent methods in all cases.
 List of table ii中文摘要 iv英文摘要 v1. Introduction……………………………………………………………………12. Preliminaries.………………………………………………………………33. The Proposed Method…………………………………………………54. Simulation…………………………………………………………………………8 4.1 Generating the bivariate current status data based on a copula model…8 4.2 Simulation studies………………………………………………95. Discussion………………………………………………………………………12Appendix A………………………………………………………………………………13Appendix B………………………………………………………………………………14References………………………………………………………………………………19
 [1] Aragon, J., Rabinowitz, D. and Tsiatis, A. (1995), “Regression With Interval Censored Data,” Biometrika, 82, 501–513.[2] Ayer, M., Brunk, H. D., Ewing, G. M., Reid, W. T. and Silverman, E. (1995), “An Empirical Distribution for Sampling with Incomplete Observations,” The Annals of Mathematical Statistics, 26, 641-647.[3] Cheng, G. and Wang, X. (2011), “Semiparametric Additive Transformation Model Under Current Status Data,” Electronic Journal of Statistics, 5, 1735-1764.[4] Clayton, D. G. (1978), “A Model for Association in Bivariate Life Table and Its Application in Epidemiological Atudies of Familial Tendency in Chronic Disease Incidence,” Biometrika, 65, 141-151.[5] Ding, A. A. and Wang, W. (2000), “On Assessing the Association for Bivariate Current Status Data,” Biometrika, 87, 879–893.[6] Ding, A. A. and Wang, W. (2004), “Testing Independence for Bivariate Current Status Data,” Journal of the American Statistical Association, 99, 145-155[7] Finkelstein, D. M. (1986), “A Proportional Hazards Model for Interval Censored Failure Time Data,” Biometrika, 42, 845-854.[8] Genest, C. (1987), “Frank’s Family of Bivariate Distributions,” Biometrika, 74,549–555.[9] Groeneboom, P. and Wellner, J. A. (1992), Information Bounds and Non-Parametric Maximum Likelihood Estimation, Boston: Birkhauser.[10] Hsu, L. and Prentice, R. L. (1996), “A Generalization of Mantel-Haenszel Test to Bivariate Failure Time Data,” Biometrika, 83, 905–911.[11] Huang, J. and Wellner, J. A. (1995), “Asymptotic Normality of the NPMLE of Linear Functionals for Interval Censored Data, Case 1,” Statistica Neeriandica, 49, 153–163.[12] Lam, K. F. and Xue, H. (2005), “A Semiparametric Regression Cure Model with Current Status Data,” Biometrika, 92, 573-586.[13] Lin, D. Y., Oakes, D. and Ying, Z. (1998), “Additive Hazards Regression with Current Status Data,” Biometrika, 85, 289–298.[14] Louis, T. A. and Shih, J. H. (1996), “Tests of Independence for Bivariate Survival Data,” Biometrics, 52, 1440–1449.[15] Oakes, D. (1982), “A Concordance Test for Independence in the Presence of Bivariate Censoring,” Biometrics, 38, 451–455.[16] Rossini, A. J. and Tsiatis, A. A. (1996), “A Semiparametric Proportional Odds Regression Model for the Analysis of Current Status Data,” Journal of the American Statistical Association, 91, 713–721.[17] Tsai, W. Y. and Wong, K. F. (2004), “A Generalization of Mantel-Haenszel Test to Bivariate Current Status Data”. Technical Report, Institute of Statistic National University of Kaohsiung.[18] Turnbull, B. W. (1976), “The Empirical Distribution Function With Arbitrarily Grouped, Censored and Truncated Data,” Journal of the Royal Statistical Society, Ser. B, 38, 290–295.
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