CHANGE POINT ANALYSIS IN HEAVY TAILED OBSERVATIONS

Reza Habibi (Iran)

Received January 30, 2009

Abstract

This paper considers the change point analysis for parameters when observations are from a heavy tailed distribution (regularly varying tails). The presence of a change point is tested and the asymptotic null distribution of test statistics is derived. Under the alternative hypothesis, the asymptotic distribution of test statistics and the consistency of change point estimators are studied. We derive the limiting distribution of change point estimators under the locally alternative. We mostly assume that the observations are in the domain of attraction of a stable distribution with index  This paper extends some of existing results in the estimation of parameters of stable distributions to change point setting.

Keywords and phrases: Brownian bridge, change point, heavy tailed observations, stable bridge, stable process.