Displaying similar documents to “On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane”

Estimating an even spherical measure from its sine transform

Lars Michael Hoffmann (2009)

Applications of Mathematics

Similarity:

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.

On set covariance and three-point test sets

Jan Rataj (2004)

Czechoslovak Mathematical Journal

Similarity:

The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of ℝ d is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives...