Average-Width Optimality for Confidence Bands in Simple Linear Regression

Piegorsch, Walter W.

doi:10.1080/01621459.1985.10478170

Cited by 12 publications

(6 citation statements)

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“…Naiman, 1983, 1984, Piegorsch, 1985a The average width of a simultaneous confidence band has been used by several authors (e.g. Naiman, 1983, 1984, Piegorsch, 1985a as a criterion for the comparison of different confidence bands. In this paper, the area of the confidence set corresponding to a confidence band is used as a new criterion.…”

Section: Introductionmentioning

confidence: 99%

Minimum Area Confidence Set Optimality for Confidence Bands in Simple Linear Regression

Liu

Hayter

2007

Journal of the American Statistical Association

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The average width of a simultaneous confidence band has been used by several authors (e.g. Naiman, 1983, 1984, Piegorsch, 1985a The average width of a simultaneous confidence band has been used by several authors (e.g. Naiman, 1983, 1984, Piegorsch, 1985a as a criterion for the comparison of different confidence bands. In this paper, the area of the confidence set corresponding to a confidence band is used as a new criterion. Furthermore, if one needs a confidence band over a finite interval of the covariate, then a restricted hyperbolic band can again be recommended, although a three-segment band may be very slightly superior in certain cases.

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Section: Introductionmentioning

confidence: 99%

Minimum Area Confidence Set Optimality for Confidence Bands in Simple Linear Regression

Liu

Hayter

2007

Journal of the American Statistical Association

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“…Gafarian (1964) imposed and Graybill & Bowden (1967) imposed c 2,2,1 = c 2,2,2 . This extra constraint may also be based on certain optimality criteria, such as the average width optimality considered by Naiman (1983, 1984) and Piegorsch (1985) among others, or the minimum area confidence set optimality considered by Liu & Hayter (2007). Of course, the average width or minimum area confidence set optimality can be used to compare two confidence bands and/or to identify the optimal confidence band.…”

Section: Discussionmentioning

confidence: 99%

Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model

Liu¹,

Lin²,

Piegorsch³

2008

Int Statistical Rev

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SummaryWe center attention on the three most recognized shapes: hyperbolic, two-segment, and three-segment (which is also referred to as a trapezoidal shape and includes a constant-width band as a special case). Some of these expressions have already appeared in the statistics literature, and some are newly derived in this article. The derivations typically involve a standard bivariate t random vector and its polar coordinate transformation.

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“…Since the original contribution by Working and Hotelling (), the literature on simultaneous confidence bands has grown vastly. Decision‐theoretic contributions include Naiman (; ), Piegorsch (; ), and the comprehensive list of references in Liu (). Despite the large body of work and a plethora of simultaneous confidence bands available, there are few concrete recommendations for practitioners outside the linear regression model.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous confidence bands: Theory, implementation, and an application to SVARs

Olea

Plagborg‐Møller

2018

J of Applied Econometrics

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Simultaneous confidence bands are versatile tools for visualizing estimation uncertainty for parameter vectors, such as impulse response functions. In linear models, it is known that that the sup-t confidence band is narrower than commonly used alternatives-for example, Bonferroni and projection bands. We show that the same ranking applies asymptotically even in general nonlinear models, such as vector autoregressions (VARs). Moreover, we provide further justification for the sup-t band by showing that it is the optimal default choice when the researcher does not know the audience's preferences. Complementing existing plug-in and bootstrap implementations, we propose a computationally convenient Bayesian sup-t band with exact finite-sample simultaneous credibility. In an application to structural VAR impulse response function estimation, the sup-t band-which has been surprisingly overlooked in this setting-is at least 35% narrower than other off-the-shelf simultaneous bands.

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Average-Width Optimality for Confidence Bands in Simple Linear Regression

Cited by 12 publications

References 11 publications

Minimum Area Confidence Set Optimality for Confidence Bands in Simple Linear Regression

Minimum Area Confidence Set Optimality for Confidence Bands in Simple Linear Regression

Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model

Simultaneous confidence bands: Theory, implementation, and an application to SVARs

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