A Model-Free Procedure for Fr\'echet Change Point Detection

Change point detection is to identify any abrupt distributional change within an independent and meaningful-ordered data sequence. As the type of data becomes more and more diversified in the modern world, we propose a method to detect change points that can be applied to a sequence of observations that reside in a general metric space. Our approach is model-free and can be used to detect both single and multiple change points. Consistency is established for the estimated change points. Both simulation and real data examples in different metric spaces are used to illustrate its competitive finite sample performance.