Testing against a high-dimensional alternative in the generalized linear model: asymptotic type I error control

Jelle J. Goeman, Hans C. van Houwelingen and Livio Finos

Biometrika, 2011, vol. 98, issue 2, 381-390

Abstract: Testing a low-dimensional null hypothesis against a high-dimensional alternative in a generalized linear model may lead to a test statistic that is a quadratic form in the residuals under the null model. Using asymptotic arguments, we show that the distribution of such a test statistic can be approximated by a ratio of quadratic forms in normal variables, for which algorithms are readily available. For generalized linear models, the asymptotic distribution shows good control of type I error for moderate to small samples, even when the number of covariates in the model far exceeds the sample size. Copyright 2011, Oxford University Press.

Date: 2011
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