Nonparametric detection of changepoints for sequentially observed data

Assume that independent data Xn1,...,Xnk(n) are observed sequentially in time, where k(n) < [infinity] is a finite horizon. Suppose also that there exists [theta] [set membership, variant] (0, 1] such that Xn1,..., Xn[k(n)[theta]] have distribution [nu]1,n and Xn[k(n)[theta]]+1,...,Xnk(n) have distribution [nu]2,n. The distributions and the changepoint [theta] are unknown. Our aim is to react as soon as possible after the change has taken place. We propose a nonparametric stopping rule which attains a given probability of "false alarm" on the one hand and, on the other hand, is less than or equal to with probability one.