IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v453y2016icp162-172.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116001898
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2016.02.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dong Hee Suh, 2018. "An Entropy Approach to Regional Differences in Carbon Dioxide Emissions: Implications for Ethanol Usage," Sustainability, MDPI, vol. 10(1), pages 1-11, January.
    2. Mingdou Zhang & Hang Xiao & Dongqi Sun & Yu Li, 2018. "Spatial Differences in and Influences upon the Sustainable Development Level of the Yangtze River Delta Urban Agglomeration in China," Sustainability, MDPI, vol. 10(2), pages 1-13, February.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stanley Smith & Scott Cody, 2013. "Making the Housing Unit Method Work: An Evaluation of 2010 Population Estimates in Florida," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 32(2), pages 221-242, April.
    2. Andrew Patton, 2002. "(IAM Series No 001) On the Out-Of-Sample Importance of Skewness and Asymetric Dependence for Asset Allocation," FMG Discussion Papers dp431, Financial Markets Group.
    3. Diana, Tony, 2011. "Improving schedule reliability based on copulas: An application to five of the most congested US airports," Journal of Air Transport Management, Elsevier, vol. 17(5), pages 284-287.
    4. Christian Caamaño-Carrillo & Javier E. Contreras-Reyes, 2022. "A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions," Mathematics, MDPI, vol. 10(9), pages 1-17, May.
    5. Mattrand, C. & Bourinet, J.-M., 2014. "The cross-entropy method for reliability assessment of cracked structures subjected to random Markovian loads," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 171-182.
    6. R. Y. Rubinstein, 2005. "A Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-event Estimation," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 5-50, March.
    7. Kin-Ping Hui, 2011. "Cooperative Cross-Entropy method for generating entangled networks," Annals of Operations Research, Springer, vol. 189(1), pages 205-214, September.
    8. Mathieu Balesdent & Jérôme Morio & Loïc Brevault, 2016. "Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 197-216, March.
    9. Annette Jacoby & Peter Lobo & Joseph J. Salvo, 2021. "Estimating Postcensal Household Size for NYC’s Neighborhoods," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 40(3), pages 459-474, June.
    10. Tran, Cong Quoc & Keyvan-Ekbatani, Mehdi & Ngoduy, Dong & Watling, David, 2021. "Stochasticity and environmental cost inclusion for electric vehicles fast-charging facility deployment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    11. Xi Chen & Enlu Zhou, 2015. "Population model-based optimization," Journal of Global Optimization, Springer, vol. 63(1), pages 125-148, September.
    12. Murray D. Smith, 2005. "Using Copulas to Model Switching Regimes with an Application to Child Labour," The Economic Record, The Economic Society of Australia, vol. 81(s1), pages 47-57, August.
    13. Lvyang Qiu & Shuyu Li & Yunsick Sung, 2021. "3D-DCDAE: Unsupervised Music Latent Representations Learning Method Based on a Deep 3D Convolutional Denoising Autoencoder for Music Genre Classification," Mathematics, MDPI, vol. 9(18), pages 1-17, September.
    14. Zhou, Yuekuan & Zheng, Siqian, 2020. "Climate adaptive optimal design of an aerogel glazing system with the integration of a heuristic teaching-learning-based algorithm in machine learning-based optimization," Renewable Energy, Elsevier, vol. 153(C), pages 375-391.
    15. Akimoto, Youhei & Auger, Anne & Hansen, Nikolaus, 2022. "An ODE method to prove the geometric convergence of adaptive stochastic algorithms," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 269-307.
    16. Anastasia Spiliopoulou & Ioannis Papamichail & Markos Papageorgiou & Yannis Tyrinopoulos & John Chrysoulakis, 2017. "Macroscopic traffic flow model calibration using different optimization algorithms," Operational Research, Springer, vol. 17(1), pages 145-164, April.
    17. 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.
    18. Zhang, Yali & Shang, Pengjian, 2019. "Multivariate multiscale distribution entropy of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 72-80.
    19. Chen, Siliang & Chen, Kang & Zhu, Xu & Jin, Xinqiao & Du, Zhimin, 2022. "Deep learning-based image recognition method for on-demand defrosting control to save energy in commercial energy systems," Applied Energy, Elsevier, vol. 324(C).
    20. A. Gouda & T. Szántai, 2008. "Rare event probabilities in stochastic networks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 441-461, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:453:y:2016:i:c:p:162-172. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.