Sequential estimation in finite-state Markov processes
S. Trybuła (1982)
Applicationes Mathematicae
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S. Trybuła (1982)
Applicationes Mathematicae
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Ryszard Magiera (2001)
Applicationes Mathematicae
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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...
Jürgen Franz (1985)
Banach Center Publications
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Eisenbaum, Nathalie (2005)
Electronic Journal of Probability [electronic only]
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Marta Ferreira (2013)
Discussiones Mathematicae Probability and Statistics
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In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the usual estimation procedure based on an i.i.d. setting may fall short of the desired precision. ...
Birgit Gaschler (1996)
Metrika
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R. Magiera, R. Różanski (1985)
Banach Center Publications
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R. Magiera (1984)
Applicationes Mathematicae
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Jiří Kopecký, Tomáš Mrkvička (2016)
Applications of Mathematics
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The pure and modified Bayesian methods are applied to the estimation of parameters of the Neyman-Scott point process. Their performance is compared to the fast, simulation-free methods via extensive simulation study. Our modified Bayesian method is found to be on average 2.8 times more accurate than the fast methods in the relative mean square errors of the point estimates, where the average is taken over all studied cases. The pure Bayesian method is found to be approximately as good...
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 ...
K. Arndt, P. Franken (1979)
Applicationes Mathematicae
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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...
R. Magiera (1977)
Applicationes Mathematicae
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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.
Wolfgang Winkler (1985)
Banach Center Publications
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G. Kallianpur, V. Mandrekar (1974)
Annales de l'institut Fourier
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We obtain necessary and sufficient conditions in order that a Gaussian process of many parameters (more generally, a generalized Gaussian random field in ) possess the Markov property relative to a class of open sets. The method adopted is the Hilbert space approach initiated by Cartier and Pitt. Applications are discussed.