Title: Change point detection by filtered derivative with $p$-Value: Choice of the extra-parameters
Authors: Pierre Bertrand - University Clermont-Ferrand (France)
Doha Hadouni - Blaise Pascal (France) [presenting]
Abstract: The study deals with off-line change point detection using the Filtered Derivative with $p$-Value method. The FD$p$V method is a two-step procedure for change point analysis. The first step is based on 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 step, we compute the $p$-value for each change point in order to retain only the true positives and discard the false positives. We give a way to estimate the optimal extra-parameters of the function FD, in order to have the fewest possible false positives and non-detected change points. Furthermore, we give the threshold of the $p$-value such that we detect only the real change points. Indeed, the estimated potential change points may differ slightly from the theoretically correct ones. After setting the extra-parameter in the two steps, we need to know whether the absence of detection or the false alarm has more impact on the Mean Integrated Square Error, which prompts us to calculate the MISE in both cases. Finally, a simulation study with a Monte Carlo method and the applications on the real data of heart-rate beat show the positive and negative ways the parametrisation can affect the results.