| Summary: | 碩士 === 國立中正大學 === 統計科學所 === 98 === In this thesis, we focus on estimation and test of conditional Kendall’s tau under semi-competing risks data and truncation data. We apply the Inverse Probability Censoring Weighted (IPCW) technique to construct an estimator of conditional Kendall’s tau, τc. We provide a test statistic for H0 : τc = τ0, where τ0 ∈ (−1, 1). When X and Y are quasi-independent, it implies τc = 0. Thus, H0 : τc = 0 is a proxy for quasi-independent. Tsai (1990), and Martin and Betensky (2005) also consider the testing problem for quasi-independence. We compare three test statistics for quasi-independence in simulation studies. Furthermore, we provide the large sample properties for our proposed estimator. We also examine the performance of the proposed estimator and the suggested test statistic via simulations. Finally, we provide two real data analyses for illustration.
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