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Rights statement: This is the author’s version of a work that was accepted for publication in Statistics & Probability Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Statistics & Probability Letters, 122, 2016 DOI: 10.1016/j.spl.2016.10.032

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## Computation of an exact confidence set for a maximum point of a univariate polynomial function in a given interval

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Computation of an exact confidence set for a maximum point of a univariate polynomial function in a given interval. / Zhou, Sanyu; Wan, Fang; Liu, Wei; Bretz, Frank.

In: Statistics and Probability Letters, Vol. 122, 03.2017, p. 157-161.

Research output: Contribution to journalJournal articlepeer-review

### Author

Zhou, Sanyu ; Wan, Fang ; Liu, Wei ; Bretz, Frank. / Computation of an exact confidence set for a maximum point of a univariate polynomial function in a given interval. In: Statistics and Probability Letters. 2017 ; Vol. 122. pp. 157-161.

### Bibtex

@article{8331ccf9a3354f9798a42a94947e50ea,
title = "Computation of an exact confidence set for a maximum point of a univariate polynomial function in a given interval",
abstract = "Construction of a confidence set for a maximum point of a function is an important statistical problem. Wan et al., (2015) provided an exact 1−α1−α confidence set for a maximum point of a univariate polynomial function in a given interval. In this paper, we give an efficient computational method for computing the confidence set of Wan et al., (2015). We demonstrate with two examples that the new method is substantially more efficient than the proposals by Wan et al., (2015). Matlab programs have been written which make the implementation of the new method straightforward.",
keywords = "Confidence set, Numerical quadrature, P-value, Statistical inference, Parametric regression, Semi-parametric regression",
author = "Sanyu Zhou and Fang Wan and Wei Liu and Frank Bretz",
note = "This is the author{\textquoteright}s version of a work that was accepted for publication in Statistics & Probability Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Statistics & Probability Letters, 122, 2016 DOI: 10.1016/j.spl.2016.10.032",
year = "2017",
month = mar,
doi = "10.1016/j.spl.2016.10.032",
language = "English",
volume = "122",
pages = "157--161",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier",

}

### RIS

TY - JOUR

T1 - Computation of an exact confidence set for a maximum point of a univariate polynomial function in a given interval

AU - Zhou, Sanyu

AU - Wan, Fang

AU - Liu, Wei

AU - Bretz, Frank

N1 - This is the author’s version of a work that was accepted for publication in Statistics & Probability Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Statistics & Probability Letters, 122, 2016 DOI: 10.1016/j.spl.2016.10.032

PY - 2017/3

Y1 - 2017/3

N2 - Construction of a confidence set for a maximum point of a function is an important statistical problem. Wan et al., (2015) provided an exact 1−α1−α confidence set for a maximum point of a univariate polynomial function in a given interval. In this paper, we give an efficient computational method for computing the confidence set of Wan et al., (2015). We demonstrate with two examples that the new method is substantially more efficient than the proposals by Wan et al., (2015). Matlab programs have been written which make the implementation of the new method straightforward.

AB - Construction of a confidence set for a maximum point of a function is an important statistical problem. Wan et al., (2015) provided an exact 1−α1−α confidence set for a maximum point of a univariate polynomial function in a given interval. In this paper, we give an efficient computational method for computing the confidence set of Wan et al., (2015). We demonstrate with two examples that the new method is substantially more efficient than the proposals by Wan et al., (2015). Matlab programs have been written which make the implementation of the new method straightforward.

KW - Confidence set

KW - P-value

KW - Statistical inference

KW - Parametric regression

KW - Semi-parametric regression

U2 - 10.1016/j.spl.2016.10.032

DO - 10.1016/j.spl.2016.10.032

M3 - Journal article

VL - 122

SP - 157

EP - 161

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -