${\mit \Gamma }$-minimax sequential estimation for Markov-additive processes

Volume 28 / 2001

Ryszard Magiera Applicationes Mathematicae 28 (2001), 467-485 MSC: Primary 62L12; Secondary 62F15, 62C20. DOI: 10.4064/am28-4-7


The problem of estimating unknown parameters of Markov-additive processes from data observed up to a random stopping time is considered. To the problem of estimation, the intermediate approach between the Bayes and the minimax principle is applied in which it is assumed that a vague prior information on the distribution of the unknown parameters is available. The loss in estimating is assumed to consist of the error of estimation (defined by a weighted squared loss function) as well as a cost of observing the process up to a stopping time. Several classes of optimal sequential procedures are obtained explicitly in the case when the available information on the prior distribution is restricted to a set ${\mit \Gamma }$ which is determined by certain moment-type conditions imposed on the prior distributions.


  • Ryszard MagieraInstitute of Mathematics
    Wroc/law University of Technology
    Wybrze/ze Wyspia/nskiego 27
    50-370 Wroc/law, Poland

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