Ancillarity properties of generalized residuals with applications in failure time models |
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| Institution: | 1. Department of Mathematics, University of Nevada, Reno, Nevada, USA;2. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403, USA;1. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, K1S 5B6, Ontario, Canada;2. Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, N2L 3G1, Ontario, Canada;1. Department of Biostatistics, Epidemiology and Environmental Health Sciences, JPH College of Public Health, Georgia Southern University, GA, 30460, USA;2. Department of Statistics, Georgia State University, Atlanta, GA, 30303, USA;1. IST and CEMAT, Lisbon, Portugal;2. Center for Mathematics and Applications (NOVA Math) and Department of Mathematics, NOVA FCT, Caparica, Portugal |
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| Abstract: | This paper addresses the issue of when residuals from failure time models, which are useful in model validation and diagnostics, possess a conditional ancillarity property. This property states that the distribution of the residuals depends on the model parameters only through a many-to-one function of these parameters, which in certain models turn out to be the censoring proportion. Concrete results are obtained for models which possess an invariance structure, and these results are applied to commonly used failure time models. Aside from furthering our understanding of the distributional structure of residuals, this conditional ancillarity property can be exploited to study in a more efficient manner the distributional properties of residuals either analytically and/or through numerical methods. |
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