Estimation of summary characteristics from replicated spatial point processes

Zbyněk Pawlas

Displaying similar documents to “Estimation of summary characteristics from replicated spatial point processes”

Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction

Tomáš Mrkvička, François Goreaud, Joël Chadoeuf (2011)

Kybernetika

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We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model...

Estimators of the asymptotic variance of stationary point processes - a comparison

Michaela Prokešová (2011)

Kybernetika

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We investigate estimators of the asymptotic variance $σ^{2}$ of a $d$ –dimensional stationary point process $Ψ$ which can be observed in convex and compact sampling window $W_{n} = n W$ . Asymptotic variance of $Ψ$ is defined by the asymptotic relation $V a r (Ψ (W_{n})) \sim σ^{2} | W_{n} |$ (as $n \to \infty$ ) and its existence is guaranteed whenever the corresponding reduced covariance measure $γ_{red}^{(2)} (\cdot)$ has finite total variation. The three estimators discussed in the paper are the kernel estimator, the estimator based on the second order intesity of the point process...

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...

An empirical evaluation of small area estimators.

Álex Costa, Albert Satorra, Eva Ventura (2003)

SORT

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This paper compares five small area estimators. We use Monte Carlo simulation in the context of both artificial and real populations. In addition to the direct and indirect estimators, we consider the optimal composite estimator with population weights, and two composite estimators with estimated weights: one that assumes homogeneity of within area variance and squared bias and one that uses area-specific estimates of variance and squared bias. In the study with real population, we found...

An alternative analysis of variance.

Nicholas T. Longford (2008)

SORT

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The one-way analysis of variance is a staple of elementary statistics courses. The hypothesis test of homogeneity of the means encourages the use of the selected-model based estimators which are usually assessed without any regard for the uncertainty about the outcome of the test. We expose the weaknesses of such estimators when the uncertainty is taken into account, as it should be, and propose synthetic estimators as an alternative.