Dr. Vasudevan Mangalam (UCSB)

Title: Asymptotic Properties of Functions of Order Statistics

Abstract: Here we consider limiting properties of average of a function of order statistics of random vectors. Almost sure limit is established under fairly mild regularity conditions, without assuming that the sequence of random vectors are i.i.d, but with the weaker assumption that the components of the random vectors are individually i.i.d. random variables. It is shown that the limit does not depend on the joint distribution. Asymptotic normality is established under the assumption that the random vectors are i.i.d.