On minimax sequential procedures for exponential families of stochastic processes

Magiera, Ryszard. "On minimax sequential procedures for exponential families of stochastic processes." Applicationes Mathematicae 25.1 (1998): 1-18. <http://eudml.org/doc/219192>.

@article{Magiera1998,
abstract = {The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of diffusions, for estimating the mean or drift coefficients of the class of Ornstein-Uhlenbeck processes, for estimating the drift of a geometric Brownian motion and for estimating a parameter of a family of counting processes. A class of minimax sequential rules for a compound Poisson process with multinomial jumps is also found.},
author = {Magiera, Ryszard},
journal = {Applicationes Mathematicae},
keywords = {Bayes sequential estimation; minimax sequential procedure; exponential family of processes; stopping time; sequential decision procedure; sequential decision; minimax sequential estimation; exponential families of diffusions; Ornstein-Uhlenbeck processes; counting processes; compound Poisson process},
language = {eng},
number = {1},
pages = {1-18},
title = {On minimax sequential procedures for exponential families of stochastic processes},
url = {http://eudml.org/doc/219192},
volume = {25},
year = {1998},
}

TY - JOUR
AU - Magiera, Ryszard
TI - On minimax sequential procedures for exponential families of stochastic processes
JO - Applicationes Mathematicae
PY - 1998
VL - 25
IS - 1
SP - 1
EP - 18
AB - The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of diffusions, for estimating the mean or drift coefficients of the class of Ornstein-Uhlenbeck processes, for estimating the drift of a geometric Brownian motion and for estimating a parameter of a family of counting processes. A class of minimax sequential rules for a compound Poisson process with multinomial jumps is also found.
LA - eng
KW - Bayes sequential estimation; minimax sequential procedure; exponential family of processes; stopping time; sequential decision procedure; sequential decision; minimax sequential estimation; exponential families of diffusions; Ornstein-Uhlenbeck processes; counting processes; compound Poisson process
UR - http://eudml.org/doc/219192
ER -