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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.
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 -