Accurate Parametric Inference for Small Samples
Alessandra R. Brazzale and Anthony C. Davison
Source: Statist. Sci. Volume 23, Number 4 (2008), 465-484.
Abstract
We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical asymptotic approximations, the focus of this paper is not on theory but on implementation and applications. Numerical illustrations are given for logistic regression, nonlinear models, and linear non-normal models, and we describe a sampling approach for the third of these classes. In the case of logistic regression, we argue that approximations are often more appropriate than ‘exact’ procedures, even when these exist.
Keywords: Conditional inference; heteroscedasticity; logistic regression; Lugannani–Rice formula; Markov chain Monte Carlo; nonlinear model; R; regression-scale model; saddlepoint approximation; spline; statistical computing
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Permanent link to this document: http://projecteuclid.org/euclid.ss/1242049390
Digital Object Identifier: doi:10.1214/08-STS273
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