Globally robust confidence intervals for simple linear regression

Jorge Adrover and Matias Salibian-Barrera

Computational Statistics & Data Analysis, 2010, vol. 54, issue 12, 2899-2913

Abstract: It is well known that when the data may contain outliers or other departures from the assumed model, classical inference methods can be seriously affected and yield confidence levels much lower than the nominal ones. This paper proposes robust confidence intervals and tests for the parameters of the simple linear regression model that maintain their coverage and significance level, respectively, over whole contamination neighbourhoods. This approach can be used with any consistent regression estimator for which maximum bias curves are tabulated, and thus it is more widely applicable than previous proposals in the literature. Although the results regarding the coverage level of these confidence intervals are asymptotic in nature, simulation studies suggest that these robust inference procedures work well for small samples, and compare very favourably with earlier proposals in the literature.

Date: 2010
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