Model averaged tail area confidence intervals in nested linear regression models

Abstract

The 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.