On the inconsistency of Bayesian non-parametric estimators in competing risks/multiple decrement models |
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Authors: | Barry C. Arnold Patrick L. Brockett William Torrez A.Larry Wright |
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Affiliation: | Department of Statistics, University of California, Riverside, CA 92521, USA;Department of Finance and Applied Research Laboratories, The University of Texas at Austin, Austin, TX 78712, USA;Department of Statistics, University of California, Riverside, CA 92521, USA;Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA |
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Abstract: | In the competing risks/multiple decrement model, the joint distribution is often not identifiable given only the observed time of failure and the cause of failure. The traditional approach is consequently to assume a parametric model. In this paper we shall not do this, but rather assume a Bayesian stance, take a Dirichlet process as a prior distribution, and then calculate the posterior distribution given the data. In this paper we show that in dimensions ? 2, the posterior mean yields an inconsistent estimator of the joint probability law, contrary to the common assumption that the prior law ‘washes out’ with large samples. For single decrement mortality tables however, the non-parametric Bayesian method allows a flexible method for adjusting a standard mortality table to reflect mortality experience, or covariate information. |
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Keywords: | Bayesian nonparametric analysis Dirichlet stochastic process Multiple decrement life tables Consistency |
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