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A note on estimating the change-point of a gradually changing stochastic process


  • Aue, Alexander
  • Steinebach, Josef


We consider an estimator of the change-point of a stochastic process satisfying some weak invariance principles. Making use of the known asymptotics of the approximating Wiener processes we derive various limiting distributions according to different orders of magnitude of the underlying change. The results take into account, but also extend those of Husková (J. Statist. Plann. Infer. 76 (1999) 109-125), who studied a location model for gradual changes with independent, identically distributed (iid) errors. Aim of this note is to show that corresponding results hold also true in our more general setting.

Suggested Citation

  • Aue, Alexander & Steinebach, Josef, 2002. "A note on estimating the change-point of a gradually changing stochastic process," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 177-191, January.
  • Handle: RePEc:eee:stapro:v:56:y:2002:i:2:p:177-191

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    Cited by:

    1. Maik Döring & Uwe Jensen, 2015. "Smooth change point estimation in regression models with random design," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 595-619, June.


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