*Tid:***4 april 2005 kl 1515-1700 **

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Erik Brodin,
Matematisk statistik,
Chalmers tekniska högskola.
**

**Titel:** **
On quantile estimation
**

* Sammanfattning: *
In the seminar I will talk about new methodology for quantile
estimation.

For quantiles within the range of the sample we use non-parametric estimation, based on linear combinations of order statistics, so-called L-estimators. First we improve on the Harrell-Davis estimator by smoothing techniques. We also prove central limit theorems for the Harrell-Davis estimator and our improvements of it. Then we use exact bootstrap to construct an optimal L-estimator in the mean square error sense.

For quantiles out of the sample we use parametric estimation, based on second order regular variation techniques. The purpose of this is to lower bias resulting from poor speed of convergence, by means of incorporating that speed into the model. First we use second order regular variation together with cross validation. Then we use perturbed Generalized Pareto distributions to model second order regular variation.