Finite sample properties of confidence intervals centered on a model averaged estimator

Kabaila, Paul; Welsh, A. H.; Wijethunga, Christeen

doi:10.1016/j.jspi.2019.10.004

Cited by 4 publications

(2 citation statements)

References 16 publications

(33 reference statements)

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“…The distribution of post-selection and post-averaging estimators are complicated, as seen in Section 5, with limits being nonlinear mixtures of normals. Supplementing such estimators with accurate confidence analysis is a challenging affair, see, e.g., Efron (2014); Hjort (2014); Kabaila et al (2019). Partial solutions are considered in Claeskens and Hjort (2008, chp.…”

Section: Discussionmentioning

confidence: 99%

Confidence Distributions for FIC Scores

Cunen

Hjort

2020

Econometrics

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When using the Focused Information Criterion (FIC) for assessing and ranking candidate models with respect to how well they do for a given estimation task, it is customary to produce a so-called FIC plot. This plot has the different point estimates along the y-axis and the root-FIC scores on the x-axis, these being the estimated root-mean-square scores. In this paper we address the estimation uncertainty involved in each of the points of such a FIC plot. This needs careful assessment of each of the estimators from the candidate models, taking also modelling bias into account, along with the relative precision of the associated estimated mean squared error quantities. We use confidence distributions for these tasks. This leads to fruitful CD–FIC plots, helping the statistician to judge to what extent the seemingly best models really are better than other models, etc. These efforts also lead to two further developments. The first is a new tool for model selection, which we call the quantile-FIC, which helps overcome certain difficulties associated with the usual FIC procedures, related to somewhat arbitrary schemes for handling estimated squared biases. A particular case is the median-FIC. The second development is to form model averaged estimators with weights determined by the relative sizes of the median- and quantile-FIC scores.

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Section: Discussionmentioning

confidence: 99%

Confidence Distributions for FIC Scores

Cunen

Hjort

2020

Econometrics

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“…He then considered a confidence interval, with nominal coverage

1-\alpha

, centred on this estimator and with half‐width equal to the

1-\alpha /2

quantile of a standard normal distribution multiplied by an estimate of this delta method approximation. The performances, in terms of coverage and expected length, of this confidence interval and the frequentist model averaged confidence interval of Buckland, Burnham & Augustin (1997), together with the variants of Burnham & Anderson (2002) and Lukacs, Burnham & Anderson (2010), were assessed by (Kabaila & Wijethunga 2019a; Kabaila & Wijethunga 2019b) and Kabaila, Welsh & Wijethunga (2020), using a testbed consisting of two nested linear regression models. These assessments illustrate the difficulty of finding confidence intervals that perform better than the standard confidence interval obtained by fitting the full model.…”

Section: Introductionmentioning

confidence: 99%

Model averaged tail area confidence intervals in nested linear regression models

Kabaila,

Perera

2023

Aus NZ J of Statistics

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SummaryThe performance, in terms of coverage and expected length, of the model averaged tail area (MATA) confidence interval, proposed by Turek & Fletcher (2012, Computational Statistics & Data Analysis, 56, 2809–2815), depends greatly on the data‐based model weights used in its construction. We generalise the computationally convenient exact formulae due to Kabaila, Welsh & Abeysekera (2016, Scandinavian Journal of Statistics, 43, 35–48) for the coverage and expected length of this confidence interval for two nested linear regression models to the case of two or more nested linear regression models. This permits the numerical assessment of the performance, in terms of coverage probability and scaled expected length, of the MATA confidence interval for any given data‐based model weights in the context of three or more nested linear regression models. We illustrate this numerical assessment of performance of the MATA confidence interval, for model weights based on any given Generalised Information Criterion, in the context of three nested linear regression models using the real life ‘Cholesterol’ data. This provides a very informative further exploration of the influence of these model weights on the performance of this confidence interval.

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Confidence intervals centred on bootstrap smoothed estimators: an impossibility result

Kabaila

Wijethunga

2023

Stat Papers

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Finite sample properties of confidence intervals centered on a model averaged estimator

Cited by 4 publications

References 16 publications

Confidence Distributions for FIC Scores

Confidence Distributions for FIC Scores

Model averaged tail area confidence intervals in nested linear regression models

Confidence intervals centred on bootstrap smoothed estimators: an impossibility result

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