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

Anaya-Izquierdo, Karim; Critchley, Frank; Marriott, Paul and Vos, Paul (2016). On the Geometric Interplay Between Goodness-of-Fit and Estimation: Illustrative Examples. In: Nielsen, Frank; Critchley, Frank and Dodson, Christopher T. J. eds. Computational Information Geometry: For Image and Signal Processing. Signals and Communication Technology. Cham: Springer, pp. 63–77.

DOI: https://doi.org/10.1007/978-3-319-47058-0_3

Abstract

We show how information geometry throws new light on the interplay between goodness-of-fit and estimation, a fundamental issue in statistical inference. A geometric analysis of simple, yet representative, models involving the same population parameter compellingly establishes the main theme of the paper: namely, that goodness-of-fit is necessary but not sufficient for model selection. Visual examples vividly communicate this. Specifically, for a given estimation problem, we define a class of least-informative models, linking these to both nonparametric and maximum entropy methods. Any other model is then seen to involve an informative rotation, often embodying extra-data considerations. We also look at the way that translation of models generates a form of bias-variance trade-off. Overall, our approach is a global extension of pioneering local work by Copas and Eguchi which, we note, was also geometrically inspired.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI