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Bayes sequential estimation procedures for exponential-type processes

100%

Magiera R.

Applicationes Mathematicae

1993-1995

tom 22

nr 3

311-320

The Bayesian sequential estimation problem for an exponential family of processes is considered. Using a weighted square error loss and observing cost involving a linear function of the process, the Bayes sequential procedures are derived.

On minimax sequential procedures for exponential families of stochastic processes

88%

Magiera R.

Applicationes Mathematicae

1998-1999

tom 25

nr 1

1-18

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.

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2 Applicationes Mathematicae

2 Magiera R.

1 1998

1 1994

Wyniki wyszukiwania

Bayes sequential estimation procedures for exponential-type processes

On minimax sequential procedures for exponential families of stochastic processes