Une méthode simple et flexible de réduction du biais des estimateurs de maximum de vraisemblance des distributions GEV avec applications aux régressions hédoniques et à d'autres processus à valeurs extrêmes
(2011)
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- Authors
- Supervisors
- Weiserbs, Daniel
- Abstract
- (en) Among the various heavy-tailed probability distributions, the GEV has the unique property of nesting the three possible limiting distributions of a series of block maxima. In practice, however, one rarely deals with large samples so that the estimators, whether obtained by MLE or by a method of moments, are generally substantially biased yielding poor predictions in the tails of the distribution. In this dissertation, we propose an alternative method of estimation (AGEV), which, in a pseudo maximum likelihood setting, reduces the bias and offers several other advantages with respect to the traditional methods. In chapter 1, using Monte Carlo simulations, we analyze the statistical properties of the AGEV in small and medium size samples. The most frequent applications of the GEV are univariate analysis in the fields of hydrology and finance. In chapter 2, we apply the AGEV to the floods of the Ourthe River basin. We first take each site separately and, next, consider them as a system of simultaneous regressions. In chapter 3 and 4, we show the usefulness of our approach for the estimation of hedonic prices, respectively the prices of great wines from the Bordeaux region and the residential rents in Louvain-la-Neuve. Chapter 5 consists in an application in the field of insurance. We model the cost of automobile damages supported by a large Belgian company controlling for the available driver’s characteristics. Since our approach can be applied to any distribution for which an explicit form exists, we apply it to the 4-parameters generalization of the Burr distribution. We find that it outperforms the GEV only in the case of the car damages (with a sample of nearly 1200 observations.)
- Affiliations
Citations
Scourneau, V. (2011). Une méthode simple et flexible de réduction du biais des estimateurs de maximum de vraisemblance des distributions GEV avec applications aux régressions hédoniques et à d’autres processus à valeurs extrêmes. https://hdl.handle.net/2078.5/150133