On the minimum coverage probability of model averaged tail area confidence intervals

Kabaila, Paul

doi:10.1002/cjs.11349

Cited by 15 publications

(10 citation statements)

References 18 publications

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“…This caveat is similar to that given by [ 11 ] for the MATA-Wald interval [ 8 ]. Likewise, in general the MATA approach to constructing a model-averaged confidence interval does not guarantee that the coverage will be exactly as desired, even if the distributional assumptions underlying its use are met [ 8 , 12 , 13 ].…”

Section: Discussionmentioning

confidence: 99%

“…It is therefore a natural choice in settings where it is reasonable to assume that the full model is closest to “truth”, as in a designed experiment. Previous studies of model-averaged confidence intervals, both theoretical and simulation-based, have also suggested that use of AIC weights is preferable to those based on AICc or BIC [ 7 , 11 – 13 ].…”

Section: Introductionmentioning

confidence: 99%

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Studentized bootstrap model-averaged tail area intervals

et al. 2019

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In many scientific studies, the underlying data-generating process is unknown and multiple statistical models are considered to describe it. For example, in a factorial experiment we might consider models involving just main effects, as well as those that include interactions. Model-averaging is a commonly-used statistical technique to allow for model uncertainty in parameter estimation. In the frequentist setting, the model-averaged estimate of a parameter is a weighted mean of the estimates from the individual models, with the weights typically being based on an information criterion, cross-validation, or bootstrapping. One approach to building a model-averaged confidence interval is to use a Wald interval, based on the model-averaged estimate and its standard error. This has been the default method in many application areas, particularly those in the life sciences. The MA-Wald interval, however, assumes that the studentized model-averaged estimate has a normal distribution, which can be far from true in practice due to the random, data-driven model weights. Recently, the model-averaged tail area Wald interval (MATA-Wald) has been proposed as an alternative to the MA-Wald interval, which only assumes that the studentized estimate from each model has a N(0, 1) or t-distribution, when that model is true. This alternative to the MA-Wald interval has been shown to have better coverage in simulation studies. However, when we have a response variable that is skewed, even these relaxed assumptions may not be valid, and use of these intervals might therefore result in poor coverage. We propose a new interval (MATA-SBoot) which uses a parametric bootstrap approach to estimate the distribution of the studentized estimate for each model, when that model is true. This method only requires that the studentized estimate from each model is approximately pivotal, an assumption that will often be true in practice, even for skewed data. We illustrate use of this new interval in the analysis of a three-factor marine global change experiment in which the response variable is assumed to have a lognormal distribution. We also perform a simulation study, based on the example, to compare the lower and upper error rates of this interval with those for existing methods. The results suggest that the MATA-SBoot interval can provide better error rates than existing intervals when we have skewed data, particularly for the upper error rate when the sample size is small.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Studentized bootstrap model-averaged tail area intervals

et al. 2019

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“…These frequentist model averaged CIs have endpoints that are smooth functions of the data; the CI centred on the bootstrap smoothed estimator has endpoints that are smoother functions of the data than the post‐model‐selection CI. However, these CIs are not guaranteed to have the specified minimum coverage probability and may not have the attractive expected length features A1 and A2 of the post‐model‐selection CI (Hjort & Claeskens ; Kabaila, Welsh & Abeysekera ; Kabaila, Welsh & Mainzer ; Kabaila ; Kabaila & Wijethunga 2019a,b).…”

Section: Introductionmentioning

confidence: 99%

An alternative to confidence intervals constructed after a Hausman pretest in panel data

Kabaila

Mainzer

2019

Aus NZ J of Statistics

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Consider panel data modelled by a linear random intercept model that includes a timevarying covariate. Suppose that our aim is to construct a confidence interval for the slope parameter. Commonly, a Hausman pretest is used to decide whether this confidence interval is constructed using the random effects model or the fixed effects model. This post-model-selection confidence interval has the attractive features that it (a) is relatively short when the random effects model is correct and (b) reduces to the confidence interval based on the fixed effects model when the data and the random effects model are highly discordant. However, this confidence interval has the drawbacks that (i) its endpoints are discontinuous functions of the data and (ii) its minimum coverage can be far below its nominal coverage probability. We construct a new confidence interval that possesses these attractive features, but does not suffer from these drawbacks. This new confidence interval provides an intermediate between the post-model-selection confidence interval and the confidence interval obtained by always using the fixed effects model. The endpoints of the new confidence interval are smooth functions of the Hausman test statistic, whereas the endpoints of the post-model-selection confidence interval are discontinuous functions of this statistic.

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“…The evaluation of an integral of the form (1) also occurs in the computation of the coverage probabilities of post-model-selection confidence intervals, frequentist model averaged confidence intervals and other non-standard confidence regions (Farchione and Kabaila 2008;Kabaila and Farchione 2012;Kabaila et al 2016;Kabaila et al 2017;Abeysekera and Kabaila 2017;Kabaila 2018). In all of these papers, this evaluation has previously been carried out by first truncating the integral (the truncation error is easily bounded) and then applying an adaptive numerical integration method.…”

Section: Introductionmentioning

confidence: 99%

Computation of the expected value of a function of a chi-distributed random variable

Kabaila¹,

Ranathunga²

2019

Preprint

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We consider the problem of numerically evaluating the expected value of a smooth bounded function of a chi-distributed random variable, divided by the square root of the number of degrees of freedom. This problem arises in the contexts of simultaneous inference, the selection and ranking of populations and in the evaluation of multivariate t probabilities. It also arises in the assessment of the coverage probability and expected volume properties of the some non-standard confidence regions. We use a transformation put forward by Mori, followed by the application of the trapezoidal rule. This rule has the remarkable property that, for suitable integrands, it is exponentially convergent. We use it to create a nested sequence of quadrature rules, for the estimation of the approximation error, so that previous evaluations of the integrand are not wasted. The application of the trapezoidal rule requires the approximation of an infinite sum by a finite sum. We provide a new easily computed upper bound on the error of this approximation. Our overall conclusion is that this method is a very suitable candidate for the computation of the coverage and expected volume properties of non-standard confidence regions.

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On the minimum coverage probability of model averaged tail area confidence intervals

Cited by 15 publications

References 18 publications

Studentized bootstrap model-averaged tail area intervals

Studentized bootstrap model-averaged tail area intervals

An alternative to confidence intervals constructed after a Hausman pretest in panel data

Computation of the expected value of a function of a chi-distributed random variable

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