Di Caterina, Claudia and Kosmidis, Ioannis (2019) Location-adjusted Wald statistics for scalar parameters. Computational Statistics & Data Analysis, 138 . pp. 126-142. doi:10.1016/j.csda.2019.04.004 ISSN 0167-9473.

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Abstract

Inference about a scalar parameter of interest is a core statistical task that has attracted immense research in statistics. The Wald statistic is a prime candidate for the task, on the grounds of the asymptotic validity of the standard normal approximation to its finite-sample distribution, simplicity and low computational cost. It is well known, though, that this normal approximation can be inadequate, especially when the sample size is small or moderate relative to the number of parameters. A novel, algebraic adjustment to the Wald statistic is proposed, delivering significant improvements in inferential performance with only small implementation and computational overhead, predominantly due to additional matrix multiplications. The Wald statistic is viewed as an estimate of a transformation of the model parameters and is appropriately adjusted, using either maximum likelihood or reduced-bias estimators, bringing its expectation asymptotically closer to zero. The location adjustment depends on the expected information, an approximation to the bias of the estimator, and the derivatives of the transformation, which are all either readily available or easily obtainable in standard software for a wealth of models. An algorithm for the implementation of the location-adjusted Wald statistics in general models is provided, as well as a bootstrap scheme for the further scale correction of the location-adjusted statistic. Ample analytical and numerical evidence is presented for the adoption of the location-adjusted statistic in prominent modelling settings, including inference about log-odds and binomial proportions, logistic regression in the presence of nuisance parameters, beta regression, and gamma regression. The location-adjusted Wald statistics are used for the construction of significance maps for the analysis of multiple sclerosis lesions from MRI data.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Journal or Publication Title:	Computational Statistics & Data Analysis
Publisher:	Elsevier Science Ltd
ISSN:	0167-9473
Official Date:	October 2019
Dates:	Date Event October 2019 Published 16 April 2019 Available 5 April 2019 Accepted
Volume:	138
Page Range:	pp. 126-142
DOI:	10.1016/j.csda.2019.04.004
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	20 September 2019
Date of first compliant Open Access:	20 September 2019
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID EP/N510129/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 TU/B/000082 Alan Turing Institute http://dx.doi.org/10.13039/100012338 2015EASZFS_003 Ministero dell’Istruzione, dell’Università e della Ricerca http://dx.doi.org/10.13039/501100003407

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