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Generalized Cross Entropy Method for estimating joint distribution from incomplete information

Author

Listed:
  • Xu, Hai-Yan
  • Kuo, Shyh-Hao
  • Li, Guoqi
  • Legara, Erika Fille T.
  • Zhao, Daxuan
  • Monterola, Christopher P.

Abstract

Obtaining a full joint distribution from individual marginal distributions with incomplete information is a non-trivial task that continues to challenge researchers from various domains including economics, demography, and statistics. In this work, we develop a new methodology referred to as “Generalized Cross Entropy Method” (GCEM) that is aimed at addressing the issue. The objective function is proposed to be a weighted sum of divergences between joint distributions and various references. We show that the solution of the GCEM is unique and global optimal. Furthermore, we illustrate the applicability and validity of the method by utilizing it to recover the joint distribution of a household profile of a given administrative region. In particular, we estimate the joint distribution of the household size, household dwelling type, and household home ownership in Singapore. Results show a high-accuracy estimation of the full joint distribution of the household profile under study. Finally, the impact of constraints and weight on the estimation of joint distribution is explored.

Suggested Citation

  • Xu, Hai-Yan & Kuo, Shyh-Hao & Li, Guoqi & Legara, Erika Fille T. & Zhao, Daxuan & Monterola, Christopher P., 2016. "Generalized Cross Entropy Method for estimating joint distribution from incomplete information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 162-172.
    • Handle: RePEc:eee:phsmap:v:453:y:2016:i:c:p:162-172
    DOI: 10.1016/j.physa.2016.02.023
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    References listed on IDEAS

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    1. Guoqi Li & Daxuan Zhao & Yi Xu & Shyh-Hao Kuo & Hai-Yan Xu & Nan Hu & Guangshe Zhao & Christopher Monterola, 2015. "Entropy Based Modelling for Estimating Demographic Trends," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-19, September.
    2. Salois, Matthew J., 2013. "Regional changes in the distribution of foreign aid: An entropy approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2893-2902.
    3. Contreras-Reyes, Javier E., 2014. "Asymptotic form of the Kullback–Leibler divergence for multivariate asymmetric heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 200-208.
    4. Matt Ruther & Galen Maclaurin & Stefan Leyk & Barbara Buttenfield & Nicholas Nagle, 2013. "Validation of spatially allocated small area estimates for 1880 Census demography," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 29(22), pages 579-616.
    5. Charles Romeo, 2005. "Estimating Discrete Joint Probability Distributions for Demographic Characteristics at the Store Level Given Store Level Marginal Distributions and a City-Wide Joint Distribution," Quantitative Marketing and Economics (QME), Springer, vol. 3(1), pages 71-93, January.
    6. Stanley Smith & June Nogle & Scott Cody, 2002. "A regression approach to estimating the average number of persons per household," Demography, Springer;Population Association of America (PAA), vol. 39(4), pages 697-712, November.
    7. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
    8. Monterola, Christopher, et al, 2002. "Accurate Forecasting of the Undecided Population in a Public Opinion Poll," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(6), pages 435-449, September.
    9. Miller, Douglas J. & Liu, Wei-han, 2002. "On the recovery of joint distributions from limited information," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 259-274, March.
    10. David Swanson & George Hough, 2012. "An Evaluation of Persons per Household (PPH) Estimates Generated by the American Community Survey: A Demographic Perspective," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 31(2), pages 235-266, April.
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    3. Muhammad Hafeez & Chunhui Yuan & Issam Khelfaoui & Almalki Sultan Musaad O & Muhammad Waqas Akbar & Liu Jie, 2019. "Evaluating the Energy Consumption Inequalities in the One Belt and One Road Region: Implications for the Environment," Energies, MDPI, vol. 12(7), pages 1-15, April.

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