Γ-minimax sequential estimation for Markov-additive processes

Ryszard Magiera. "Γ-minimax sequential estimation for Markov-additive processes." Applicationes Mathematicae 28.4 (2001): 467-485. <http://eudml.org/doc/278851>.

@article{RyszardMagiera2001,
abstract = {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 Γ which is determined by certain moment-type conditions imposed on the prior distributions.},
author = {Ryszard Magiera},
journal = {Applicationes Mathematicae},
keywords = {gamma-minimax estimation; Bayes estimation; minimax estimation; stopping time; sequential procedure; Markov-additive process},
language = {eng},
number = {4},
pages = {467-485},
title = {Γ-minimax sequential estimation for Markov-additive processes},
url = {http://eudml.org/doc/278851},
volume = {28},
year = {2001},
}

TY - JOUR
AU - Ryszard Magiera
TI - Γ-minimax sequential estimation for Markov-additive processes
JO - Applicationes Mathematicae
PY - 2001
VL - 28
IS - 4
SP - 467
EP - 485
AB - 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 Γ which is determined by certain moment-type conditions imposed on the prior distributions.
LA - eng
KW - gamma-minimax estimation; Bayes estimation; minimax estimation; stopping time; sequential procedure; Markov-additive process
UR - http://eudml.org/doc/278851
ER -