English   -  Français  

Résumé de communication

Résumé 177 :

Some asymptotics for elemental sets in regression with applications
Knight, Keith
University of Toronto

In a linear regression model, elemental sets consist of the minimum number of observations needed to estimate the regression parameter where the resulting estimators are called elemental estimators. Elemental estimators have a long history in statistics; many estimators are functions of elemental estimators and elemental estimators are used for outlier detection as well as for computation of highly robust estimators. In this paper, we consider some asymptotic theory for elemental sets in linear regression. In particular, we derive the limiting distribution of the elemental sets that produce "good" elemental estimators. A number of applications of this theory are also given, including a diagnostic for homoscedasticity and an algorithm for sampling elemental sets in the computation of least median of squares estimates.