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

Ryszard Magiera¹

¹ Institute of Mathematics Wroc/law University of Technology Wybrze/ze Wyspia/nskiego 27 50-370 Wroc/law, Poland

Applicationes Mathematicae, Tome 28 (2001) no. 4, pp. 467-485

Résumé

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.

Détail

DOI : 10.4064/am28-4-7

Keywords: problem estimating unknown parameters markov additive processes observed random stopping time considered problem estimation intermediate approach between bayes minimax principle applied which assumed vague prior information distribution unknown parameters available loss estimating assumed consist error estimation defined weighted squared loss function cost observing process stopping time several classes optimal sequential procedures obtained explicitly available information prior distribution restricted set mit gamma which determined certain moment type conditions imposed prior distributions