Asymptotic Behavior of Estimators for One Change-Point Detection Based on Processes Whose Kernel Function Has Degree Greater than Two

We study change-point estimation for absolutely continuous independent and identically distributed random variables from a nonparametric point of view. We define a sequence of processes and estimators based on U-statistics, whose kernel function has a degree greater than two. We then propose to extend the results in the literature on the asymptotic behavior of a sequence of processes and estimators, in the case of the existence or not of a change point. Numerical simulations are provided to support the theoretical results.