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Interval estimation: An information theoretic approach

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  • Amos Golan
  • Aman Ullah

Abstract

We develop here an alternative information theoretic method of inference of problems in which all of the observed information is in terms of intervals. We focus on the unconditional case in which the observed information is in terms the minimal and maximal values at each period. Given interval data, we infer the joint and marginal distributions of the interval variable and its range. Our inferential procedure is based on entropy maximization subject to multidimensional moment conditions and normalization in which the entropy is defined over discretized intervals. The discretization is based on theory or empirically observed quantities. The number of estimated parameters is independent of the discretization so the level of discretization does not change the fundamental level of complexity of our model. As an example, we apply our method to study the weather pattern for Los Angeles and New York City across the last century.

Suggested Citation

  • Amos Golan & Aman Ullah, 2017. "Interval estimation: An information theoretic approach," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 781-795, October.
    • Handle: RePEc:taf:emetrv:v:36:y:2017:i:6-9:p:781-795
    DOI: 10.1080/07474938.2017.1307573
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    References listed on IDEAS

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    1. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    2. Judge,George G. & Mittelhammer,Ron C., 2012. "An Information Theoretic Approach to Econometrics," Cambridge Books, Cambridge University Press, number 9780521869591, January.
    3. Judge,George G. & Mittelhammer,Ron C., 2012. "An Information Theoretic Approach to Econometrics," Cambridge Books, Cambridge University Press, number 9780521689731, January.
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    Cited by:

    1. Sun, Yuying & Zhang, Xinyu & Wan, Alan T.K. & Wang, Shouyang, 2022. "Model averaging for interval-valued data," European Journal of Operational Research, Elsevier, vol. 301(2), pages 772-784.
    2. Piao Wang & Shahid Hussain Gurmani & Zhifu Tao & Jinpei Liu & Huayou Chen, 2024. "Interval time series forecasting: A systematic literature review," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(2), pages 249-285, March.
    3. Chen, Simiao & Prettner, Klaus & Kuhn, Michael & Bloom, David E., 2021. "The economic burden of COVID-19 in the United States: Estimates and projections under an infection-based herd immunity approach," The Journal of the Economics of Ageing, Elsevier, vol. 20(C).
    4. Sun, Yuying & Han, Ai & Hong, Yongmiao & Wang, Shouyang, 2018. "Threshold autoregressive models for interval-valued time series data," Journal of Econometrics, Elsevier, vol. 206(2), pages 414-446.
    5. Haowen Bao & Yongmiao Hong & Yuying Sun & Shouyang Wang, 2024. "Sparse Interval-valued Time Series Modeling with Machine Learning," Papers 2411.09452, arXiv.org.

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