ASYMPTOTIC THEORY FOR THE MAXIMUM LIKELIHOOD ESTIMATE OF THE CHANGE-POINT UNDER CONTIGUITY

摘要

The problem of estimating an unknown change-point in the parameters of a sequence of independent d-dimensional time-series valued random variables from a general parametric family of distributions is considered. Adapting the estimation methodology that Hinkley pursued for the case of abrupt changes, we develop theory for deriving the asymptotic distribution of the maximum likelihood estimator of the change-point under the contiguity condition. The contiguity assumption we impose here is quite similar to that found in the literature. We apply the methodology to estimate the change-point for the daily log-returns data of Verizon (VZ) and BellSouth (BLS) from the NYSE.