Displaying similar documents to “Estimating an even spherical measure from its sine transform”

Estimation variances for parameterized marked Poisson processes and for parameterized Poisson segment processes

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...

Estimation of intersection intensity in a Poisson process of segments

Tomáš Mrkvička (2007)

Commentationes Mathematicae Universitatis Carolinae

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The minimum variance unbiased estimator of the intensity of intersections is found for stationary Poisson process of segments with parameterized distribution of primary grain with known and unknown parameters. The minimum variance unbiased estimators are compared with commonly used estimators.

On an estimation problem for type I censored spatial Poisson processes

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.

On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane

Tomáš Mrkvička, Jan Rataj (2009)

Kybernetika

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A method of estimation of intrinsic volume densities for stationary random closed sets in ℝ d based on estimating volumes of tiny collars has been introduced in T. Mrkvička and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch. Proc. Appl. 118 (2008), 2, 213-231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation...