Convergence of Dirichlet Measures Arising in Context of Bayesian Analysis of Competing Risks Models
✍ Scribed by Victor H. Salinas-Torres; Carlos A. de Bragança Pereira; Ram C. Tiwari
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 336 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0047-259X
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✦ Synopsis
In this paper, we study the weak convergence of Dirichlet measures on the class constituted by vectors of subprobability measures such that the sum of its components is a probability measure on a complete separable metric space. This vectorial class of subprobabilities appears in the context of the competing risks theory and the Dirichlet measures are considered as a prior family in a Bayesian approach. The weak convergence results are derived and used to study the convergence of the Bayes estimators of certain parameters in competing risks models. 1997 Academic Press
1. Introduction
Let (X, A) be a complete separable metric space endowed with the corresponding Borel _-field, and let P be the class of all subprobability measures on (X, A). Let P 1 and P 2 be copies of P, and define P*= [(P 1 * , P 2 *) # P 1 _P 2 : P 1 *+P 2 * is a probability measure on (X, A)]. Let _(P 1 _P 2 ) be the product _-field, _(P 1 )__(P 2 ), where _(P i ) is the smallest _-field in P i such that the map P* [ P*(A) from P i into [0, 1] is _(P i )measurable for each A # A, i=1, 2. Clearly, P i is a complete separable metric space under the weak convergence (cf. Prohorov, 1956) and we article no. MV971679 24 0047-259XÂ97 25.00