Confidence Intervals in Regression That Utilize Uncertain Prior Information About a Vector Parameter

Kabaila, Paul; Tissera, Dilshani

doi:10.1111/anzs.12090

Cited by 9 publications

(9 citation statements)

References 41 publications

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“…A numerical constrained optimization approach to the construction of valid confidence intervals and sets that utilize uncertain prior information has been applied by Farchione and Kabaila (2008), Kabaila and Giri (2009a), Kabaila and Giri (2013), Kabaila and Giri (2014), Kabaila and Tissera (2014) and Abeysekera and Kabaila (2017). In each case, numerical constrained optimization was performed using programs written in MATLAB, restricting the accessibility of these confidence intervals and sets.…”

Section: Discussionmentioning

confidence: 99%

ciuupi: An R package for Computing Confidence Intervals that Utilize Uncertain Prior Information

Mainzer¹,

Kabaila²

2019

The R Journal

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We have created the R package ciuupi to compute confidence intervals that utilize uncertain prior information in linear regression. Unlike post-model-selection confidence intervals, the confidence interval that utilizes uncertain prior information (CIUUPI) implemented in this package has, to an excellent approximation, coverage probability throughout the parameter space that is very close to the desired minimum coverage probability. Furthermore, when the uncertain prior information is correct, the CIUUPI is, on average, shorter than the standard confidence interval constructed using the full linear regression model. In this paper we provide motivating examples of scenarios where the CIUUPI may be used. We then give a detailed description of this interval and the numerical constrained optimization method implemented in R to obtain it. Lastly, using a real data set as an illustrative example, we show how to use the functions in ciuupi.Y. L. Tseng and L. D. Brown. Good exact confidence sets for a multivariate normal mean.

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Section: Discussionmentioning

confidence: 99%

ciuupi: An R package for Computing Confidence Intervals that Utilize Uncertain Prior Information

Mainzer¹,

Kabaila²

2019

The R Journal

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“…Mead [1] and Hinkelmann and Kempthorne [2] discussed how the higher order interactions of factorial experiments are believed to be negligible. Kabaila and Tesseri [3] reinforced that this kind of believe on the higher order interactions is the basis for fractional factorial experiments. To make valid inference on the remaining parameters, the uncertainty in the assumption of negligible interactions of any order can be represented by a hypothesis and conduct an appropriate test to remove the uncertainty (cf.…”

Section: Introductionmentioning

confidence: 94%

“…Unlike the classical and cell mean models, the regression model based method has the advantage of fitting the model in the presence of missing values or even with unbalanced data. The regression model for the response, Y of a 2 3 factorial experiment without any replication can be written as…”

Section: Introductionmentioning

confidence: 99%

“…Khan [17]; Saleh [16]; Yunus [18]). Kabaila and Dharmarathne [6] and Kabaila and Tissera [3] used NSPI to construct confidence intervals for regression parameters. In this paper, we express the data from a factorial experiment as a linear model (see (1)) in order to test the coefficients of the main effects (and lower order interactions) when there is uncertain NSPI on the coefficients of higher level interactions.…”

Section: Introductionmentioning

confidence: 99%

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Tests on a Subset of Regression Parameters for Factorial Experimental Data with Uncertain Higher Order Interactions

Khan¹,

Pratikno²,

Rahman³

et al. 2019

JSTA

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The data generated by many factorial experiments are analyzed by linear regression models. Often the higher order interaction terms of such models are negligible (e.g., R. Mead, The Design of Experiments, Cambridge University Press, Cambridge, 1988, p. 368) although there is uncertainty around it. This kind of nonsample prior information (NSPI) can be presented by null hypotheses (cf. T.A. Bancroft, Ann. Math. Stat. 15 (1944), 190 204), and its uncertainty removed through appropriate statistical test. Depending on the level of the NSPI the unrestricted, restricted, and pretest (PTT) tests are defined. The sampling distributions of test statistics and power functions of the three tests are derived. The graphical and analytical comparisons of powers reveal that the PTT dominates over the other tests.

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“…We shift the focus from the scaled volume (or its p'th root) to the scaled expected volume of the RCS. Scaled expected length has been profitably used in related problems and to resolve a paradox in decisiontheoretic interval estimation (Farchione and Kabaila, 2008, Kabaila and Giri, 2009, Kabaila and Tissera, 2014. Casella, Hwang and Robert (1993) show that a confidence interval for the univariate normal mean that is obtained by minimizing the posterior expected loss, for the prior distribution and the risk function that they specify, has paradoxical properties.…”

Section: Introductionmentioning

confidence: 99%

Optimized recentered confidence spheres for the multivariate normal mean

Abeysekera¹,

Kabaila²

2017

Electron. J. Statist.

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Casella and Hwang, 1983, JASA, introduced a broad class of recentered confidence spheres for the mean θ of a multivariate normal distribution with covariance matrix σ 2 I, for σ 2 known. Both the center and radius functions of these confidence spheres are flexible functions of the data. For the particular case of confidence spheres centered on the positive-part James-Stein estimator and with radius determined by empirical Bayes considerations, they show numerically that these confidence spheres have the desired minimum coverage probability 1 − α and dominate the usual confidence sphere in terms of scaled volume. We shift the focus from the scaled volume to the scaled expected volume of the recentered confidence sphere. Since both the coverage probability and the scaled expected volume are functions of the Euclidean norm of θ, it is feasible to optimize the performance of the recentered confidence sphere by numerically computing both the center and radius functions so as to optimize some clearly specified criterion. We suppose that we have uncertain prior information that θ = 0. This motivates us to determine the center and radius functions of the confidence sphere by numerical minimization of the scaled expected volume of the confidence sphere at θ = 0, subject to the constraints that (a) the coverage probability never falls below 1 − α and (b) the radius never exceeds the radius of the standard 1 − α confidence sphere. Our results show that, by focusing on this clearly specified criterion, significant gains in performance (in terms of this criterion) can be achieved. We also present analogous results for the much more difficult case that σ 2 is unknown.

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Confidence Intervals in Regression That Utilize Uncertain Prior Information About a Vector Parameter

Cited by 9 publications

References 41 publications

ciuupi: An R package for Computing Confidence Intervals that Utilize Uncertain Prior Information

ciuupi: An R package for Computing Confidence Intervals that Utilize Uncertain Prior Information

Tests on a Subset of Regression Parameters for Factorial Experimental Data with Uncertain Higher Order Interactions

Optimized recentered confidence spheres for the multivariate normal mean

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