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Interval estimation: An information theoretic approach


  • Amos Golan
  • Aman Ullah


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

    1. Judge,George G. & Mittelhammer,Ron C., 2012. "An Information Theoretic Approach to Econometrics," Cambridge Books, Cambridge University Press, number 9780521869591.
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    Cited by:

    1. 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.

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