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B1585
Title: Change point detection by filtered derivative with $p-$Value: Choice of the extra-parameters and the impact on MISE Authors:  Pierre Bertrand - University Clermont-Ferrand (France)
Doha Hadouni - Blaise Pascal (France) [presenting]
Abstract: The Filtered Derivative with $p-$Value method (FDpV) is a two-step procedure for change point analysis. In the first step, we use the Filtered Derivative function (FD) to select a set of potential change points, using its extra-parameters - namely the threshold for detection, and the sliding window size. In the second one, we calculate the $p-$value for each change point in order to only retain the true positives and discard the false positives. We deal with off-line change point detection using the FDpV method. We give a way to estimate the optimal extra-parameters of the function FD, in order to have the fewest possible false positives (false alarms) and non-detected change points (ND). Thus, the estimated potential change points may differ slightly from the theoretically correct ones. After setting the extra-parameters, we need to know which criterion (the absence of detection or the false alarm) has more impact on the Mean Integrated Square Error (MISE). Which leads us to calculate the MISE in both cases (false alarm case and the case of non detected change point). Finally, we simulate some examples with a Monte Carlo method so we can better understand the positive and negative ways the parametrisation can affect the results.