Statistical estimation of parameters in Markov processes
O. Lange (1955)
Colloquium Mathematicae
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O. Lange (1955)
Colloquium Mathematicae
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Jan Hurt, Petr Lachout, Dietmar Pfeifer (2001)
Kybernetika
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In this paper we consider the problem of estimating the intensity of a spatial homogeneous Poisson process if a part of the observations (quadrat counts) is censored. The actual problem has occurred during a court case when one of the authors was a referee for the defense.
Jan Hurt, Wiltrud Kuhlisch (1995)
Kybernetika
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Stoimenova, Vessela (2005)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 60J80. The paper deals with a robust parametric estimation in branching processes {Zt(n)} having a random number of ancestors Z0(n) as both n and t tend to infinity (and thus Z0(n) in some sense). The offspring distribution is considered to belong to a discrete analogue of the exponential family – the class of the power series offspring distributions. Robust estimators, based on one and several sample paths, are proposed and studied...
Tomáš Mrkvička (2004)
Commentationes Mathematicae Universitatis Carolinae
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A complete and sufficient statistic is found for stationary marked Poisson processes with a parametric distribution of marks. Then this statistic is used to derive the uniformly best unbiased estimator for the length density of a Poisson or Cox segment process with a parametric primary grain distribution. It is the number of segments with reference point within the sampling window divided by the window volume and multiplied by the uniformly best unbiased estimator of the mean segment...
Yuri A. Kutoyants (2004)
SORT
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We present a review of several results concerning invariant density estimation by observations of ergodic diffusion process and some related problems. In every problem we propose a lower minimax bound on the risks of all estimators and then we construct an asymptotically efficient estimator.