Detecting change in a random sequence
This paper proposes a sequential procedure for detecting a change-point in a sequence of i.i.d. random observations \(X_ 1,X_ 2,..\). in a nonparametric framework. The sequential test statistic is based upon the empirical distribution function of variables \(E_ i\) which act as the recursive residuals in the Gaussian linear model: \(E_ i\) is the e.d.f. of the i-1 previous observations, taken at the value \(X_ i.\) Under the null hypothesis, the variables \(E_ i\) are quite uniformly distributed and the authors give the asymptotic threshold for various weighted statistics and a fixed level, using the approximation by a Kiefer process. They then prove the consistency of the proposed test.
scientific article; zbMATH DE number 4044975
scientific article