A general framework will be suggested for developing a variety of contemporary computer-intensive methods in statistics, including methods based on the bootstrap and empirical likelihood. The framework enables new connections to be drawn between different, competing approaches, and motivates new methods with more attractive properties. The relevance of these methods to curve estimation will be stressed, but it will be seen that techniques that may be used to obtain better performance when estimating a density function or a regression mean may be applied in many other settings too. Professor Peter Hall will also be giving a series of 5 lectures within the Symposium on Nonparametric Functional Estimation, organized by the CRM, from October 13 to October 24, 1997. Depending on the nature of the adjustment, the biased bootstrap can be used to reduce bias, or reduce variance, or render some characteristic equal to a predetermined quantity.
Solutions based on templates are one possibility.
As well as applications in relatively familiar statistical settings, they may be used to estimate chaotic maps when the data are observed with noise. They usually enjoy the advantage of considerable smoothness over competing nonparametric approaches. Hypothesis testing problems connected with modality will also be considered. In particular, a number of calibration methods will be discussed. 15 octobre, 17h00, salle 6245.