Convergence of Dirichlet Measures Arising in Context of Bayesian Analysis of Competing Risks Models

• Published in: Journal of multivariate analysis Vol. 62; no. 1; pp. 24 - 35
• Main Authors: Salinas-Torres, Victor H., de Bragança Pereira, Carlos A., Tiwari, Ram C.
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.07.1997; Elsevier
• Series: Journal of Multivariate Analysis
• Subjects: Bayes estimation; Dirichlet processes; Dirichlet processes weak convergence random censored model Bayes estimation; Exact sciences and technology; Limit theorems; Mathematics; Nonparametric inference; Probability and statistics; Probability theory and stochastic processes; Probability theory on algebraic and topological structures; random censored model; Sciences and techniques of general use; Statistics; weak convergence; Bayes estimation; Dirichlet processes; weak convergence; random censored model; Weak convergence; Risk model; Separable space; Metric space; Bayes analysis; Competing risk; Risk theory; Dirichlet measure; Probability measure
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1006/jmva.1997.1679

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.