Shurenkov G. The construction of estimators of change-points

The thesis is devoted to the construction of algorithms of fast search for several change-points and the study of their asymptotic properties. Nonparametric estimators of several change-points are considered in the thesis. The main attention is given to an adaptive case when estimators are constructed from the results of previous estimations. Considered estimators are called DP-estimators as they can be computed by means of dynamic programming. Estimations for mathematical expectation of the length of interval inconsistency are found. Adaptive DP-estimators for several change-points are constructed and their asymptotic properties are studied. Consistency of quantile estimators is proven, also in the case of unknown distributions. Explicit form of the distribution of median estimator of change-points is determined. The conditions under which adaptive DP-estimators are asymptotically optimal are found.