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An algorithm to construct Monte Carlo confidence intervals for an arbitrary function of probability distribution parameters

Author

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  • Hristos Tyralis
  • Demetris Koutsoyiannis
  • Stefanos Kozanis

Abstract

We derive a new algorithm for calculating an exact confidence interval for a parameter of location or scale family, based on a two-sided hypothesis test on the parameter of interest, using some pivotal quantities. We use this algorithm to calculate approximate confidence intervals for the parameter or a function of the parameter of one-parameter continuous distributions. After appropriate heuristic modifications of the algorithm we use it to obtain approximate confidence intervals for a parameter or a function of parameters for multi-parameter continuous distributions. The advantage of the algorithm is that it is general and gives a fast approximation of an exact confidence interval. Some asymptotic (analytical) results are shown which validate the use of the method under certain regularity conditions. In addition, numerical results of the method compare well with those obtained by other known methods of the literature on the exponential, the normal, the gamma and the Weibull distribution. Copyright Springer-Verlag 2013

Suggested Citation

  • Hristos Tyralis & Demetris Koutsoyiannis & Stefanos Kozanis, 2013. "An algorithm to construct Monte Carlo confidence intervals for an arbitrary function of probability distribution parameters," Computational Statistics, Springer, vol. 28(4), pages 1501-1527, August.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:4:p:1501-1527
    DOI: 10.1007/s00180-012-0364-7
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    References listed on IDEAS

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    1. Paul H. Garthwaite & Stephen T. Buckland, 1992. "Generating Monte Carlo Confidence Intervals by the Robbins–Monro Process," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 159-171, March.
    2. Grant Hillier & Mark Armstrong, 1999. "The Density of the Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 67(6), pages 1459-1470, November.
    3. Y. Román-Montoya & M. Rueda & A. Arcos, 2008. "Confidence intervals for quantile estimation using Jackknife techniques," Computational Statistics, Springer, vol. 23(4), pages 573-585, October.
    4. repec:dau:papers:123456789/1908 is not listed on IDEAS
    5. J. Hemelrijk, 1966. "Underlining random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 20(1), pages 1-7, March.
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    Cited by:

    1. Silva, Ivair R., 2017. "Confidence intervals through sequential Monte Carlo," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 112-124.

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