## Abstract

Consider the problem of obtaining a confidence interval for some function g(θ) of an unknown parameter 9, for which a (1-α)-confidence interval is given. If g(θ) is one-to-one the solution is immediate. However, if g is not one-to-one the problem is more complex and depends on the structure of g. In this note the situation where g is a nonmonotone convex function is considered. Based on some inequality, a confidence interval for g(θ) with confidence level at least 1-α is obtained from the given (1-α) confidence interval on θ. Such a result is then applied to the N(μ,σ^{2}) distribution with σ known. It is shown that the coverage probability of the resulting confidence interval, while being greater than 1-α, has in addition an upper bound which does not exceed Φ(3z_{1-α/2})-α/2.

Original language | English |
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Pages (from-to) | 89-98 |

Number of pages | 10 |

Journal | Statistical Papers |

Volume | 40 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1999 |

## Keywords

- Confidence intervals
- Convex (concave) functions

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty