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Estimation from aggregate data

Author

Listed:
  • Gouno, E.
  • Courtrai, L.
  • Fredette, M.

Abstract

A statistical methodology to handle aggregate data is proposed. Aggregate data arise in many fields such as medical science, ecology, social science, reliability, etc. They can be described as follows: individuals are moving progressively along a finite set of states and observations are made in a time window split into several intervals. At each observation time, the only available information is the number of individuals in each state and the history of each item viewed as a stochastic process is thus lost. The time spent in a given state is unknown. Using a data completion technique, an estimation of the hazard rate in each state based on sojourn times is obtained and an estimation of the survival function is deduced. These methods are studied through simulations and applied to a data set. The simulation study shows that the algorithms involved in the methods converge and are robust.

Suggested Citation

  • Gouno, E. & Courtrai, L. & Fredette, M., 2011. "Estimation from aggregate data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 615-626, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:615-626
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    References listed on IDEAS

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    1. Renshaw, Eric, 2004. "Metropolis-Hastings from a stochastic population dynamics perspective," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 765-786, May.
    2. D. L. Hawkins & Chien-Pai Han, 2000. "Estimating Transition Probabilities from Aggregate Samples Plus Partial Transition Data," Biometrics, The International Biometric Society, vol. 56(3), pages 848-854, September.
    3. Yu, Chang & Zelterman, Daniel, 2008. "Sums of exchangeable Bernoulli random variables for family and litter frequency data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1636-1649, January.
    4. B. A. Davis, 2002. "Estimating and interpolating a Markov chain from aggregate data," Biometrika, Biometrika Trust, vol. 89(1), pages 95-110, March.
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    Cited by:

    1. Jonas Knape & Kent M. Daane & Perry de Valpine, 2014. "Estimation of stage duration distributions and mortality under repeated cohort censuses," Biometrics, The International Biometric Society, vol. 70(2), pages 346-355, June.
    2. Pasanisi, Alberto & Fu, Shuai & Bousquet, Nicolas, 2012. "Estimating discrete Markov models from various incomplete data schemes," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2609-2625.

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