we are pleased to reschedule the talk by Brendan Beare to next Friday, January 31 at 6 pm at Sapienza, Department of
Statistical Sciences, Aula XIII Palazzina Tumminelli.
Speaker: Brendan K. Beare, University of Sydney
Title: Convergence in distribution of quantile, Lorenz and P-P processes via the delta method
Abstract: We establish a necessary and sufficient condition for the quantile process based on iid sampling to converge in distribution in the space $L^1(0,1)$. The condition is that the quantile function is locally absolutely continuous on the open unit interval and satisfies a slight strengthening of square integrability. For a nonzero population mean, convergence in distribution of the quantile process in $L^1(0,1)$ is shown to be sufficient, but not necessary, for convergence in distribution of the associated Lorenz process in $C[0,1]$. We further establish a necessary and sufficient condition for the P-P process based on iid sampling from two populations to converge in distribution in $L^1(0,1)$. The condition is that the P-P curve is locally absolutely continuous on the open unit interval. All demonstrations of convergence in distribution are achieved using the delta method, and therefore validate a bootstrap approximation to the relevant process as a byproduct.
Please note that Palazzina Tumminelli is the first building on the left entering from V.le dell'Università :
We look forward to seeing you there.
The Organizing Committee
Gianluca Cubadda
Massimo Franchi
Tommaso Proietti
Paolo Santucci de Magistris