Estimation and test of conditional Kendall's Tau under bivariate left-truncation data

Jin-Jian Hsieh and Zih-Jyun Li

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 13, 6635-6644

Abstract: This article focuses on estimation and test of the coordinatewise conditional Kendall's tau under bivariate left-truncation data. We apply the inverse probability censoring weighted (IPCW) technique to construct an estimator of the coordinatewise conditional Kendall's tau, τc$ \mbox{\boldmath $ \tau $} _{c}$, and provide a Wald's type test statistic to test H0:τc=τ0$H_{0}: \mbox{\boldmath $ \tau $} _{c}= \mbox{\boldmath $ \tau $} _{0}$, where the elements of τ0$ \mbox{\boldmath $ \tau $} _{0}$ are between ( − 1, 1). We examine the proposed estimator and test statistic via simulation studies. If X and T are quasi-independent, the coordinatewise conditional Kendall's tau is zero. Thus, H0:τc=0$H_{0}: \mbox{\boldmath $ \tau $} _{c}= \mbox{\boldmath $ 0 $}$ is a proxy for quasi-independence test. We compare our test statistic with Martin's test statistic (Martin and Betensky, 2005) for quasi-independence test via simulations.

Date: 2017
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DOI: 10.1080/03610926.2015.1132326

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