##
**A fast algorithm for detecting multiple changing moments.**
*(English.
Ukrainian original)*
Zbl 0935.62058

Theory Probab. Math. Stat. 57, 109-114 (1998); translation from Teor. Jmovirn. Mat. Stat. 57, 103-108 (1997).

The problem of a posterior searching of a moment of change of a distribution in a sequence of independent random variables is well studied. Less studied is the case of many changing moments. A nonparametric algorithm is known for estimation of such moments which needs \(N^{2}\) calculations, where \(N\) is the number of elements of the sequence. Also, an algorithm of dynamic programming is known with \(KN\) calculations, where \(K\) is the number of the various possible distributions of the sequence. In this paper for a dynamic nonparametric algorithm of a posterior searching of many changing moments in a sequence of independent observations, sufficient conditions are found for the rate of convergence \(A_{N}\ln N/N,\) where \(A_{N}\) is an arbitrary real sequence that tends to infinity.

Reviewer: A.V.Swishchuk (Kyïv)

### MSC:

62G20 | Asymptotic properties of nonparametric inference |

65C60 | Computational problems in statistics (MSC2010) |

62G99 | Nonparametric inference |

93E10 | Estimation and detection in stochastic control theory |