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Published in:
2022 | OriginalPaper | Chapter
18. Residual Likelihood
Author : Peter McCullagh
Published in: Ten Projects in Applied Statistics
Publisher: Springer International Publishing
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Abstract
The accommodation of correlations associated with baseline relationships is a recurrent theme in this book. For the most part, this is done using Gaussian models with several additive variance components. The preferred method for variance-component estimation is maximum likelihood based on residuals. In practice, all linear-model specifications are made in the observation space \({\mathbb R}^n\). This chapter develops the theory needed for maximum-likelihood based on residuals. That includes both point estimation of variance components, and likelihood-ratio tests either for components in the mean model or for components in the variance model. There are very few examples in applied work where measure-theoretic issues intrude into computations, but likelihood-ratio testing in this setting is one such example. The text emphasizes the role of the kernel subspace in connection with residuals, and explains how to compute a likelihood ratio keeping the kernel fixed.