B1205
Title: Self-weighted change-point test and estimator
Authors: Stefanie Schwaar - University of Kaiserslautern (Germany) [presenting]
Abstract: To detect a change in a time-series based on the pseudo-likelihood ratio the weighted CUSUM statistic was derived. This statistic involves a weight function and the absolute value of a partial sum. The weighted CUSUM tends to infinity unless it is transformed. But the convergence to the asymptotic distribution is quite slow. That is why modifications became of interest. Proper modifications can be derived by the use of a different weight function. Besides truncations also different powers of the weight function are analysed. For a class of deterministic functions sufficient conditions are determined such that the modified weighted CUSUM still has a known asymptotic distribtion. Taking a look at some of those weight functions by using different powers, we observe that for the test statistic other weight functions are preferable than for the change-point estimator. The preferable weight function depends on the position of the change, which is unknown. To overcome this problem a data driven change-point test and its estimator are proposed. We call these self-weighted change-point test and estimator. The asymptotics of the test statistic as well as the asymptotics of the estimator are presented.
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