### Abstract

An exact joint confidence set is proposed for two binomial parameters estimated from independent samples. Its construction relies on inverting the minimum volume test, a two-dimensional analogue of Sterne's test for a single probability. The algorithm involves computer-intensive exact computation based on binomial probabilities. The proposed confidence set has good coverage properties and it performs much better than the likelihood-based confidence set for the same problem. Applying the principle of intersection-union tests, the method can be used to derive exact tests and confidence intervals for functions of the two binomial parameters. Based on this, new exact unconditional two-sided confidence intervals are proposed for the risk difference and risk ratio. The performance of the new intervals is comparable to that of certain well-known confidence intervals in small samples. Extension of the methods described to two hypergeometric or two Poisson variables is straightforward.

Original language | English |
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Pages (from-to) | 5046-5053 |

Number of pages | 8 |

Journal | Computational Statistics and Data Analysis |

Volume | 52 |

Issue number | 11 |

DOIs | |

Publication status | Published - Jul 15 2008 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Statistics, Probability and Uncertainty
- Electrical and Electronic Engineering
- Computational Mathematics
- Numerical Analysis
- Statistics and Probability

### Cite this

*Computational Statistics and Data Analysis*,

*52*(11), 5046-5053. https://doi.org/10.1016/j.csda.2008.04.032

**An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions.** / Reiczigel, J.; Abonyi-Tóth, Zsolt; Singer, Júlia.

Research output: Contribution to journal › Article

*Computational Statistics and Data Analysis*, vol. 52, no. 11, pp. 5046-5053. https://doi.org/10.1016/j.csda.2008.04.032

}

TY - JOUR

T1 - An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions

AU - Reiczigel, J.

AU - Abonyi-Tóth, Zsolt

AU - Singer, Júlia

PY - 2008/7/15

Y1 - 2008/7/15

N2 - An exact joint confidence set is proposed for two binomial parameters estimated from independent samples. Its construction relies on inverting the minimum volume test, a two-dimensional analogue of Sterne's test for a single probability. The algorithm involves computer-intensive exact computation based on binomial probabilities. The proposed confidence set has good coverage properties and it performs much better than the likelihood-based confidence set for the same problem. Applying the principle of intersection-union tests, the method can be used to derive exact tests and confidence intervals for functions of the two binomial parameters. Based on this, new exact unconditional two-sided confidence intervals are proposed for the risk difference and risk ratio. The performance of the new intervals is comparable to that of certain well-known confidence intervals in small samples. Extension of the methods described to two hypergeometric or two Poisson variables is straightforward.

AB - An exact joint confidence set is proposed for two binomial parameters estimated from independent samples. Its construction relies on inverting the minimum volume test, a two-dimensional analogue of Sterne's test for a single probability. The algorithm involves computer-intensive exact computation based on binomial probabilities. The proposed confidence set has good coverage properties and it performs much better than the likelihood-based confidence set for the same problem. Applying the principle of intersection-union tests, the method can be used to derive exact tests and confidence intervals for functions of the two binomial parameters. Based on this, new exact unconditional two-sided confidence intervals are proposed for the risk difference and risk ratio. The performance of the new intervals is comparable to that of certain well-known confidence intervals in small samples. Extension of the methods described to two hypergeometric or two Poisson variables is straightforward.

UR - http://www.scopus.com/inward/record.url?scp=46549086822&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46549086822&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2008.04.032

DO - 10.1016/j.csda.2008.04.032

M3 - Article

VL - 52

SP - 5046

EP - 5053

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 11

ER -