Сhange Point Detection Based on Optimal Transportation and Geometric Discrepancy

This work was motivated by the opportunity of researching new statistical framework based on interaction between vector rank functions and generalized discrepancy. In particular, a novel semiparametric posteriori method of change point detection and estimation for multidimensional probability distributions with densities and the first two existing moments were implemented. The detection of change point is conducted by the process constructed by composition of vector rank, sliding window and discrepancy. Resulting method detects change points and provides meaningful estimates for both single and multiple change points if the data set is large enough. However, it is more impaired in case of concentric probability distributions. One of the fruitful findings of this work is the Hilbert space of measure nonuniformities which is hoped to provide iterative methods for more precise change point estimation in the future.