Nonparametric change-point estimation

Consider a sequence of independent random variables {Xi:1≤i≤n}{Xi:1≤i≤n} having cdf FF for i≤θni≤θn and cdf GG otherwise. A class of strongly consistent estimators for the change-point θ∈(0,1)θ∈(0,1) is proposed. The estimators require no knowledge of the functional forms or parametric families of FF and GG. Furthermore, FF and GG need not differ in their means (or other measure of location). The only requirement is that FF and GG differ on a set of positive probability. The proof of consistency provides rates of convergence and bounds on the error probability for the estimators. The estimators are applied to two well-known data sets, in both cases yielding results in close agreement with previous parametric analyses. A simulation study is conducted, showing that the estimators perform well even when FF and GG share the same mean, variance and skewness.