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About Massart Concentration Inequalities
<p>Model selection is a classical topic in statistics. The idea of selecting a model</p><p>via penalizing a log-likelihood type criterion goes back to the early seventies</p><p>with the pioneering works of Mallows and Akaike. One can find many consis-</p><p>tency results in the literature for such criteria. These results are asymptotic</p><p>in the sense that one deals with a given number of models and the number of</p><p>observations tends to infinity. We shall give an overview of a nonasymptotic</p><p>theory for model selection which has emerged during these last ten years. In</p><p>various contexts of function estimation it is possible to design penalized log-</p><p>likelihood type criteria with penalty terms depending not only on the number</p><p>of parameters defining each model (as for the classical criteria) but also on the</p><p>? complexity ? of the whole collection of models to be considered. The perfor-</p><p>mance of such a criterion is analyzed via non asymptotic risk bounds for the</p><p>corresponding penalized estimator which express that it performs almost as</p><p>well as if the ? best model ? (i.e. with minimal risk) were known. For practical</p><p>relevance of these methods, it is desirable to get a precise expression of the</p><p>penalty terms involved in the penalized criteria on which they are based. This</p><p>is why this approach heavily relies on concentration inequalities, the proto-</p><p>type being Talagrand’s inequality for empirical processes. Our purpose will be</p><p>to give an account of the theory and discuss some selected applications such</p><p>as variable selection or change points detection.</p>
Detailed Information
| Author: | Jean Picard |
|---|---|
| Publication Year: | 2006 |
| Pages: | 347 |
| Language: | other |
| File Size: | 1.5113 |
| Format: | |
| Price: | FREE |
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