Second-order variational equations for spatial point processes with a view to pair correlation function estimation

Orthogonal series estimation of the pair correlation function of a spatial point process

The pair correlation function is a fundamental spatial point process characteristic that, given the intensity function, determines second order moments of the point process. Non-parametric estimation of the pair correlation function is a typical initial step of a statistical analysis of a spatial point pattern. Kernel estimators are popular but especially for clustered point patterns suffer fro...

Second Order Variational Optic Flow Estimation

In this paper we present a variational approach to accurately estimate the motion vector field in a image sequence introducing a second order Taylor expansion of the flow in the energy function to be minimized. This feature allows us to simultaneously obtain, in addition, an estimation of the partial derivatives of the motion vector field. The performance of our approach is illustrated with the...

Variational Iteration Method for q-Difference Equations of Second Order

Estimation Variances for Estimators of Product Densities and Pair Correlation Functions of Planar Point Processes

Approximations of the estimation variances of kernel estimators of the pair correlation function and the product density of a planar Poisson process are given. Furthermore, a heuristic approximation of the estimation variance of an estimator of the pair correlation function of a "general" planar point process is suggested. All formulae have been tested by simulation experiments.

The variational iteration method for a class of tenth-order boundary value differential equations