Assuming the finiteness of only the second moment, we prove that LIL for Lorenz curves holds true provided that the underlying distribution function and its inverse are continuous. The proof is crucially based on a limit theorem for the general Vervaat process.

Based on an R2-valued random sample {(yi,xi),1≤i≤n} on the simple linear regression model yi=xiβ+α+εi with unknown error variables εi, least squares processes (LSPs) are introduced in D[0,1] for the unknown slope β and intercept α, as well as for the unknown β when α=0. These LSPs...

In this paper we study strong approximations (invariance principles) of the sequential uniform and general Bahadur-Kiefer processes of long-range dependent sequences. We also investigate the strong and weak asymptotic behavior of the sequential Vervaat process, i.e., the integrated sequential...