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Cross-Sectional Sampling, Bias, Dependence, and Composite Likelihood


  • Micha Mandel
  • Yosef Rinott


A population that can be joined at a known sequence of discrete times is sampled cross-sectionally, and the sojourn times of individuals in the sample are observed. It is well known that cross-sectioning leads to length-bias, but less well known that it may result also in dependence among the observations, which is often ignored. It is therefore important to understand and to account for this dependence when estimating the distribution of sojourn times in the population. In this paper, we study conditions under which observed sojourn times are independent and conditions under which treating observations as independent, using the product of marginals in spite of dependence, results in proper inference. The latter is known as the Composite Likelihood approach. We study parametric and nonparametric inference based on Composite Likelihood, and provide conditions for consistency, and further asymptotic properties, including normal and non-normal distributional limits of estimators. We show that Composite Likelihood leads to good estimators under certain conditions, and illustrate that it may fail without them. The theoretical study is supported by simulations. We apply the proposed methods to two data sets collected by cross-sectional designs: data on hospitalization time after bowel and hernia surgeries, and data on service times at our university.

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  • Micha Mandel & Yosef Rinott, 2012. "Cross-Sectional Sampling, Bias, Dependence, and Composite Likelihood," Discussion Paper Series dp614, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp614

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    References listed on IDEAS

    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, July.
    2. Chakrabarti, Subir K., 1999. "Markov Equilibria in Discounted Stochastic Games," Journal of Economic Theory, Elsevier, vol. 85(2), pages 294-327, April.
    3. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Nash Equilibrium," Discussion Paper Series dp596r, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised May 2012.
    4. Horst, Ulrich, 2005. "Stationary equilibria in discounted stochastic games with weakly interacting players," Games and Economic Behavior, Elsevier, vol. 51(1), pages 83-108, April.
    5. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    6. A. S. Nowak & T. E. S. Raghavan, 1992. "Existence of Stationary Correlated Equilibria with Symmetric Information for Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 519-526, August.
    7. Yehuda (John) Levy, 2012. "A Cantor Set of Games with No Shift-Homogeneous Equilibrium Selection," Discussion Paper Series dp607, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    8. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
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    Discrete entrance process; Length bias; Poisson cohort distribution; Truncation;

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