Nonparametric tests for the changepoint problem (Q1094781)

Let \(X_ 1,...,X_{[n\lambda \nvDash n},\quad X_{[n\lambda]+1},...,X_ n\) be independent, continuous random variables such that \(X_ i\), \(i=1,...,[n\lambda]\), have distribution H, and \(X_ i\), \(i=[n\lambda]+1,...,n\), have distribution function G. The integer [n\(\lambda\) ] refers to the changepoint of the random sequence. We propose nonparametric procedures for testing \(\lambda =1\) (no changepoint) versus \(\lambda\in (0,1)\). An asymptotically strongly consistent estimator of \(\lambda\) is also given.