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An exact confidence set for a maximum point of a univariate polynomial function in a given interval

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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An exact confidence set for a maximum point of a univariate polynomial function in a given interval. / Wan, Fang; Liu, Wei; Bretz, Frank et al.
In: Technometrics, Vol. 57, No. 4, 2015, p. 559-565.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Wan, F, Liu, W, Bretz, F & Han, Y 2015, 'An exact confidence set for a maximum point of a univariate polynomial function in a given interval', Technometrics, vol. 57, no. 4, pp. 559-565. https://doi.org/10.1080/00401706.2014.962708

APA

Wan, F., Liu, W., Bretz, F., & Han, Y. (2015). An exact confidence set for a maximum point of a univariate polynomial function in a given interval. Technometrics, 57(4), 559-565. Advance online publication. https://doi.org/10.1080/00401706.2014.962708

Vancouver

Wan F, Liu W, Bretz F, Han Y. An exact confidence set for a maximum point of a univariate polynomial function in a given interval. Technometrics. 2015;57(4):559-565. Epub 2014 Sept 17. doi: 10.1080/00401706.2014.962708

Author

Wan, Fang ; Liu, Wei ; Bretz, Frank et al. / An exact confidence set for a maximum point of a univariate polynomial function in a given interval. In: Technometrics. 2015 ; Vol. 57, No. 4. pp. 559-565.

Bibtex

@article{f205f5e5916049c481d6bf890bb570f5,
title = "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 which has many applications. In this article, an exact 1 − α confidence set is provided for a maximum point of a univariate polynomial function in a given interval. It is shown how the construction method can readily be applied to many parametric and semiparametric regression models involving a univariate polynomial function. Examples are given to illustrate this confidence set and to demonstrate that it can be substantially narrower and so better than the only other confidence set available in the statistical literature that guarantees 1 − α confidence level.",
keywords = "Parametric regression, Semiparametric regression, Statistical inference, Statistical simulation",
author = "Fang Wan and Wei Liu and Frank Bretz and Yang Han",
year = "2015",
doi = "10.1080/00401706.2014.962708",
language = "English",
volume = "57",
pages = "559--565",
journal = "Technometrics",
issn = "0040-1706",
publisher = "American Statistical Association",
number = "4",

}

RIS

TY - JOUR

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

AU - Wan, Fang

AU - Liu, Wei

AU - Bretz, Frank

AU - Han, Yang

PY - 2015

Y1 - 2015

N2 - Construction of a confidence set for a maximum point of a function is an important statistical problem which has many applications. In this article, an exact 1 − α confidence set is provided for a maximum point of a univariate polynomial function in a given interval. It is shown how the construction method can readily be applied to many parametric and semiparametric regression models involving a univariate polynomial function. Examples are given to illustrate this confidence set and to demonstrate that it can be substantially narrower and so better than the only other confidence set available in the statistical literature that guarantees 1 − α confidence level.

AB - Construction of a confidence set for a maximum point of a function is an important statistical problem which has many applications. In this article, an exact 1 − α confidence set is provided for a maximum point of a univariate polynomial function in a given interval. It is shown how the construction method can readily be applied to many parametric and semiparametric regression models involving a univariate polynomial function. Examples are given to illustrate this confidence set and to demonstrate that it can be substantially narrower and so better than the only other confidence set available in the statistical literature that guarantees 1 − α confidence level.

KW - Parametric regression

KW - Semiparametric regression

KW - Statistical inference

KW - Statistical simulation

U2 - 10.1080/00401706.2014.962708

DO - 10.1080/00401706.2014.962708

M3 - Journal article

VL - 57

SP - 559

EP - 565

JO - Technometrics

JF - Technometrics

SN - 0040-1706

IS - 4

ER -