Rank based estimators of the change-point

Abstract

Consider a sequence of independent random variables X 1,…, X n having continuous distribution function F for 1 ⩽ i ⩽ m (< n) and a different continuous distribution function G for m < i ⩽ n, where m is unknown and called the change-point. We propose two classes of estimators of the change-point m based on ranks and investigate their limit properties. The proofs rely on exchangeability of ranks which then allows the use of Hájek's (1961) results on the asymptotic behavior of simple linear rank statistics.