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Likelihood Confidence Intervals When Only Ranges Are Available

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  • Szilárd Nemes

    (Institute of Clinical Sciences, Sahlgrenska Academy, University of Gothenburg, 405 30 Gothenburg, Sweden)

Abstract

Research papers represent an important and rich source of comparative data. The change is to extract the information of interest. Herein, we look at the possibilities to construct confidence intervals for sample averages when only ranges are available with maximum likelihood estimation with order statistics (MLEOS). Using Monte Carlo simulation, we looked at the confidence interval coverage characteristics for likelihood ratio and Wald-type approximate 95% confidence intervals. We saw indication that the likelihood ratio interval had better coverage and narrower intervals. For single parameter distributions, MLEOS is directly applicable. For location-scale distribution is recommended that the variance (or combination of it) to be estimated using standard formulas and used as a plug-in.

Suggested Citation

  • Szilárd Nemes, 2019. "Likelihood Confidence Intervals When Only Ranges Are Available," Stats, MDPI, vol. 2(1), pages 1-7, February.
    • Handle: RePEc:gam:jstats:v:2:y:2019:i:1:p:8-110:d:203814
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    References listed on IDEAS

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    1. Hettmansperger, Thomas P. & Sheather, Simon J., 1986. "Confidence intervals based on interpolated order statistics," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 75-79, March.
    2. N. Balakrishnan & T. Li, 2006. "Confidence Intervals for Quantiles and Tolerance Intervals Based on Ordered Ranked Set Samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 757-777, December.
    3. Alan Hutson, 1999. "Calculating nonparametric confidence intervals for quantiles using fractional order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(3), pages 343-353.
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