Projection measures and estimation variances of intensities

The paper investigates random processes of geometrical objects in Euclidean spaces. General properties of the measure of total projections are derived by means of Palm distribution. Explicit formulas for variances of the proj ection measure are obtained for Poisson point processes of compact sets. Intensity estimators of fibre (surface) processes are then studied by means of projection measures. Classification of direct and indirect probes is in troduced. The indirect sampling design of vertical sections and projections is generalized and its statistical properties derived.