Browsing by Author "Wells, MT"

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Estimation of Kendall's tau under censoring
(2000-10-01)
Wang, WJ
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Wells, MT
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統計學研究所
;
Institute of Statistics
We study nonparametric estimation of Kendall's tau, tau, for bivariate censored data. Previous estimators of tau, proposed by Brown, Hollander and Korwar (1974), Weier and Basu (1980) and Oakes (1982), fail to be consistent when marginals are dependent. Here we express tau as an integral functional of the bivariate survival function and construct a natural estimator via the von Mises functional approach. This does not necessarily yield a consistent estimator since tail region information on the survival curve may not be identifiable due to right censoring. To assess the magnitude of the inconsistency we propose some estimable bounds on tau. It is shown that estimates of the bounds shrink to provide consistency if the largest observations on both marginal coordinates are uncensored and satisfy certain regularity conditions. The bounds depend on the sample size, on censoring rates and, in particular, on the estimated probability of the unknown tail region. We also discuss using the bootstrap method for variance estimation and bias correction. Two illustrative data examples are analyzed, as well as some simulation results.
Model selection and semiparametric inference for bivariate failure-time data
(2000-03-01)
Wang, WJ
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Wells, MT
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統計學研究所
;
Institute of Statistics
We propose model selection procedures for bivariate survival models for censored data generated by the Archimedean copula Family. In route to constructing the selection methodology, we develop estimates of some time-dependent association measures, including estimates of the local and global Kendall's tau, local odds ratio, and other measures defined throughout the literature. We propose a goodness-of-fit-base model selection methodology as well as a graphical approach. We show that the proposed methods have desirable asymptotic properties and perform well in finite samples.
Power analysis for linear models with spherical errors
(2002-11-01)
Wang, WJ
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Wells, MT
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統計學研究所
;
Institute of Statistics
In this article, we consider testing a general linear hypothesis for a regression model when the error distribution belongs to the class of spherical distributions. The distributional robustness of the F-statistics under a null hypothesis for spherically symmetric distributions is well understood. This invariance property, however, does not hold under the alternative hypothesis. Motivated by a simplified example, we study the relationship between power of the test and the error distribution's dispersion and kurtosis. We find that these two parameters are not sufficiently precise measures for determining the power behavior of a test. (C) 2002 Elsevier Science B.V. All rights reserved.