On the Geometric Interplay Between Goodness-of-Fit and Estimation: Illustrative Examples

摘要

In statistical analysis, it is common practice to end the model building phase when one, or more, goodness-of-fit tests no longer reject the hypothesis that the data generation process lies in a given parametric model. This model is, often, then treated as known, and parametric inference theory, within it, is assumed to be sufficient to describe the uncertainty in the problem. As a corollary of this, only information captured by the sufficient statistics for the final model is used in the inference. The excellent papers Eguchi and Copas (2005), Copas and Eguchi (2010), summarised below, take a first order geometric approach, which defines the envelope likelihood and a 'double the variance' rule, which are designed to capture the actual model uncertainty.