Nonparametric statistical procedures for the changepoint problem

Abstract Let X 1 ,…, X r −1 , X r , X r +1 ,…, X n be independent, continuous random variables such that X i , i = 1,…, r , has distribution function F ( x ), and X i , i = r +1,…, n , has distribution function F ( x − Δ ), with -∞ Δ r is unknown, this is refered to as a change point problem with at most one change. The unknown parameter Δ represents the magnitude of the change and r is called the changepoint. In this paper we present a general review discussion of several nonparametric approaches for making inferences about r and Δ .