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Nonparametric Priors for Vectors of Survival Functions

  • Ilenia Epifani

    (Politecnico di Milano)

  • Antonio Lijoi

    ()

    (Department of Economics and Quantitative Methods, University of Pavia, and Collegio Carlo Alberto)

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    The paper proposes a new nonparametric prior for two–dimensional vectors of survival functions (S1, S2). The definition we introduce is based on the notion of L´evy copula and it will be used to model, in a nonparametric Bayesian framework, two–sample survival data. Such an application will yield a natural extension of the more familiar neutral to the right process of Doksum (1974) adopted for drawing inferences on single survival functions. We, then, obtain a description of the posterior distribution of (S1, S2), conditionally on possibly right–censored data. As a by–product of our analysis, we find out that the marginal distribution of a pair of observations from the two samples coincides with the Marshall–Olkin or the Weibull distribution according to specific choices of the marginal L´evy measures.

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    File URL: http://economia.unipv.it/docs/dipeco/quad/ps/RePEc/pav/wpaper/q098.pdf
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    Paper provided by University of Pavia, Department of Economics and Quantitative Methods in its series Quaderni di Dipartimento with number 098.

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    Length: 31 pages
    Date of creation: May 2009
    Date of revision:
    Handle: RePEc:pav:wpaper:098
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    Web page: http://dipartimenti.unipv.eu/on-dip/epmq/Home.html

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    1. Jyotirmoy Dey & R.V. Erickson & R.V. Ramamoorthi, 2003. "Some Aspects Of Neutral To Right Priors," International Statistical Review, International Statistical Institute, vol. 71(2), pages 383-401, 08.
    2. Pierpaolo De Blasi & Giovanni Peccati & Igor Prünster, 2009. "Asymptotics for posterior hazards," Carlo Alberto Notebooks 122, Collegio Carlo Alberto.
    3. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
    4. Nieto-Barajas, Luis E. & Walker, Stephen G., 2007. "A Bayesian semi-parametric bivariate failure time model," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6102-6113, August.
    5. Walker, Stephen & Muliere, Pietro, 2003. "A bivariate Dirichlet process," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 1-7, August.
    6. David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323.
    7. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    8. Kallsen, Jan & Tankov, Peter, 2006. "Characterization of dependence of multidimensional Lévy processes using Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1551-1572, August.
    9. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Posterior analysis for some classes of nonparametric models," ICER Working Papers - Applied Mathematics Series 05-2008, ICER - International Centre for Economic Research.
    10. Rodríguez, Abel & Dunson, David B & Gelfand, Alan E, 2008. "The Nested Dirichlet Process," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1131-1154.
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