NONPARAMETRIC CHANGE-POINT ESTIMATION FOR DATA FROM AN ERGODIC SEQUENCE

In the framework of the series scheme we assume that an observations sequence {X(i)(n), 1 less than or equal to i less than or equal to n) is such that X(i)(n) = UiI(1 less than or equal to i less than or equal to [theta n]) + ViI([theta n] + 1 less than or equal to i less than or equal to n), where (U-i,V-i) is a stationary ergodic sequence the marginal distributions of which are different, and theta is a change-point in the probabilistic characteristics such that theta epsilon (0; 1). The main result of this paper is the proof of the fact that the sequence (theta n)(n greater than or equal to 1) of nonparametric estimations constructed here is consistent (theta(n)-->theta).