The
assumption of stationarity is too restrictive especially for long time series.
This paper studies the change point problem through a change point estimator
based on the φ-divergence which provides a rich set of distance
like measures between pairs of distributions. The change point problem is
considered in the following sub-fields: the problem of divergence estimation,
testing for the homogeneity between two samples as well as estimating the time
of change. The asymptotic distribution of the change point estimator is
estimated by the limiting distribution of a stochastic process within given
bounds through asymptotic theory surrounding the likelihood theory. The
distribution is found to converge to that of a standardized Brownian bridge
process.
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