Abstract
In this Note, general results on the off-line least-square estimate of changes in the mean of a stationary random process are presented. To reach this goal, a generalisation of the Hájek-Rényi inequality, dealing with the functuation of the normalized partial sums, is given: it applies to a very large class of processes. This result is used to derive the consistence and the rate of convergence of the change-point estimate, no matter if the number of changes is known or not. All these results apply to a large class of stationary processes, including strongly mixing and long-range dependent processes.
| Translated title of the contribution | Détection de ruptures multiples dans la moyenne d'un processus aléatoire |
|---|---|
| Original language | English |
| Pages (from-to) | 239-243 |
| Number of pages | 5 |
| Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |
| Volume | 324 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Jan 1997 |