Closed-form fiducial confidence intervals for some functions of independent binomial parameters with comparisons

@article{Krishnamoorthy2017ClosedformFC,
  title={Closed-form fiducial confidence intervals for some functions of independent binomial parameters with comparisons},
  author={Kalimuthu Krishnamoorthy and Meesook Lee and Dan Zhang},
  journal={Statistical Methods in Medical Research},
  year={2017},
  volume={26},
  pages={43 - 63}
}
Approximate closed-form confidence intervals (CIs) for estimating the difference, relative risk, odds ratio, and linear combination of proportions are proposed. These CIs are developed using the fiducial approach and the modified normal-based approximation to the percentiles of a linear combination of independent random variables. These confidence intervals are easy to calculate as the computation requires only the percentiles of beta distributions. The proposed confidence intervals are… 
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References

SHOWING 1-10 OF 26 REFERENCES
Inference for functions of parameters in discrete distributions based on fiducial approach: Binomial and Poisson cases
Confidence intervals for the ratio of two binomial proportions
Sometimes the ratio of two binomial proportions is the parameter of major interest, for instance as the risk ratio in a two-group cohort study (Fleiss, 1973) or as the likelihood ratio for a…
Modified Normal-based Approximation to the Percentiles of Linear Combination of Independent Random Variables with Applications
TLDR
A modified normal-based approximation for calculating the percentiles of a linear combination of independent random variables is proposed and provides simple satisfactory solutions for some classical problems and for some other problems.
Interval estimation for the difference between independent proportions: comparison of eleven methods.
TLDR
Two new approaches which also avoid aberrations are developed and evaluated, and a tail area profile likelihood based method produces the best coverage properties, but is difficult to calculate for large denominators.
Confidence Intervals for the Product of Two Binomial Parameters
Abstract Many more-or-less reasonable solutions to the problem of statistical estimation of the product P 1 P 2 of two binomial parameters by confidence intervals can be given. After specializing to…
New large-sample confidence intervals for a linear combination of binomial proportions
Approximate is Better than “Exact” for Interval Estimation of Binomial Proportions
Abstract For interval estimation of a proportion, coverage probabilities tend to be too large for “exact” confidence intervals based on inverting the binomial test and too small for the interval…
One-sided confidence intervals in discrete distributions
MOVER-R confidence intervals for ratios and products of two independently estimated quantities
  • R. Newcombe
  • Mathematics
    Statistical methods in medical research
  • 2016
TLDR
The purpose of this note is to show how the MOVER algorithm for a ratio of two independently estimated quantities requires modification to cope with the general case in which the lower and upper confidence limits for the numerator can take either sign.
A family of confidence intervals for the ratio of two binomial proportions.
TLDR
The power divergence family of statistics introduced by Cressie and Read is used to obtain approximate confidence intervals for the ratio of two proportions and small-sample comparisons of the intervals are presented.
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