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Displaying similar documents to “Sequential estimation in processes with independent increments”

Bayes sequential estimation procedures for exponential-type processes

Ryszard Magiera (1994)

Applicationes Mathematicae

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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

Ryszard Magiera (1998)

Applicationes Mathematicae

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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...

Some investigations in minimax estimation theory

Stanisław Trybuła

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1. IntroductionThough the theory of minimax estimation was originated about thirty five years ago (see [7], [8], [9], [23]), there are still many unsolved problems in this area. Several papers have been devoted to statistical games in which the set of a priori distributions of the parameter was suitably restricted ([2], [10], [13]). Recently, special attention was paid to the problem of admissibility ([24], [3], [11], [12]).This paper is devoted to the problem of determining minimax...

Sequential estimation in processes with independent increments

S. Trybuła

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CONTENTS1. Introduction...................... 52. Definitions........................... 63. Stochastic processes.................. 74. Processes with independent increments...... 85. Sequential estimation for the Poisson process..... 126. Other processes with independent increments.......... 337. Efficiency for a given value of the parameter......... 398. Final remarks........................................... 43References................................................ 45 ...

Information inequalities for the minimax risk of sequential estimators (with applications)

Lesław Gajek, B. Mizera-Florczak (1998)

Applicationes Mathematicae

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Information inequalities for the minimax risk of sequential estimators are derived in the case where the loss is measured by the squared error of estimation plus a linear functional of the number of observations. The results are applied to construct minimax sequential estimators of: the failure rate in an exponential model with censored data, the expected proportion of uncensored observations in the proportional hazards model, the odds ratio in a binomial distribution and the expectation...