When are first-order asymptotics adequate? A diagnostic

Anaya-Izquierdo, Karim; Critchley, Frank and Marriott, Paul (2014). When are first-order asymptotics adequate? A diagnostic. Stat, 3(1) pp. 17–22.

DOI: https://doi.org/10.1002/sta4.40

Abstract

This paper looks at boundary effects on inference in an important class of models including, notably, logistic regression. Asymptotic results are not uniform across such models. Accordingly, whatever their order, methods asymptotic in sample size will ultimately “break down” as the boundary is approached, in the sense that effects such as infinite skewness, discreteness and collinearity will dominate. In this paper, a highly interpretable diagnostic tool is proposed, allowing the analyst to check if the boundary is going to have an appreciable effect on standard inferential techniques.

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