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A note on Bayesian detection of change-points with an expected miss criterion


  • Karatzas Ioannis


A process X is observed continuously in time; it behaves like Brownian motion with drift, which changes from zero to a known constant ϑ>0 at some time τ that is not directly observable. It is important to detect this change when it happens, and we attempt to do so by selecting a stopping rule T* that minimizes the “expected miss” E|T−τ| over all stopping rules T. Assuming that τ has an exponential distribution with known parameter λ>0 and is independent of the driving Brownian motion, we show that the optimal rule T* is to declare that the change has occurred, at the first time t for which

Suggested Citation

  • Karatzas Ioannis, 2003. "A note on Bayesian detection of change-points with an expected miss criterion," Statistics & Risk Modeling, De Gruyter, vol. 21(1/2003), pages 3-14, January.
  • Handle: RePEc:bpj:strimo:v:21:y:2003:i:1/2003:p:3-14:n:5

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    References listed on IDEAS

    1. Hans Dietz, 2001. "Asymptotic Behaviour of Trajectory Fitting Estimators for Certain Non-ergodic SDE," Statistical Inference for Stochastic Processes, Springer, vol. 4(3), pages 249-258, October.
    2. Nakahiro Yoshida, 1990. "Asymptotic behavior of M-estimator and related random field for diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 221-251, June.
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    Cited by:

    1. Blanchet-Scalliet, Christophette & Diop, Awa & Gibson, Rajna & Talay, Denis & Tanre, Etienne, 2007. "Technical analysis compared to mathematical models based methods under parameters mis-specification," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1351-1373, May.

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