Title
Asymptotics of Clustering Criteria for Smooth Distributions
Speaker
Karthik Bharath, The Ohio State University
Abstract
We propose a clustering framework based on a criterion function, whose empirical version is an L-statistic with irregular weights comprising of a combination of heavily-trimmed sums and sample quantiles, develop the asymptotic theory and demonstrate its utility in the problem of testing for the presence of jumps in discretely observed semimartingale models used in financial applications. The testing problem serves as the leitmotif of our clustering framework and the test represents a first step towards viewing jumps occurring in such discretely observed processes as a clustering mechanism. The sample version of the criterion function, which we refer to as the Empirical Cross-over Function (ECF), indeed is not uniquely defined and as a consequence, we also examine an alternatively de fined empirical criterion function based on truncated sums which offers considerable insight into the asymptotics of the clustering mechanism and is, perhaps, more versatile.
Karthik Bharath received his PhD from the University of Connecticut in 2012 and is a visiting assistant professor in the Department of Statistics at The Ohio State University. His research interests include limit theorems in probability, empirical processes with applications in statistics and stochastic processes.
