### Alternative models in precipitation analysis.

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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 that among...

To reconstruct an even Borel measure on the unit sphere from finitely many values of its sine transform a least square estimator is proposed. Applying results by Gardner, Kiderlen and Milanfar we estimate its rate of convergence and prove strong consistency. We close this paper by giving an estimator for the directional distribution of certain three-dimensional stationary Poisson processes of convex cylinders which have applications in material science.

For a high dimensional field of random variables, global correlation is defined as the ratio of average covariance and average variance, and its elementary properties are studied. Global correlation is used to harmonize uncertainty assessments at global and local scales. It can be estimated by the correlation of random aggregations of fixed size of disjoint sets of random variables. Illustrative applications are given using crop loss per county per year and forest carbon.

Let ( ${\mathbb{S}}^{1},{d}_{{\mathbb{S}}^{1}}$ S 1 , d S 1 ) be the unit circle in ℝ2 endowed with the arclength distance. We give a sufficient and necessary condition for a general probability measure μto admit a well defined Fréchet mean on ( ${\mathbb{S}}^{1},{d}_{{\mathbb{S}}^{1}}$ S 1 , d S 1 ). We derive a new sufficient condition of existenceP(α, ϕ) with no restriction on the support of the measure. Then, we study the convergence of the empirical Fréchet mean to the Fréchet mean and we give an algorithm to compute it.

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 where explanatory...