area.mse: MSE approximation for area predictors In pgs: Precision of Geometric Sampling

Description

Compute a MSE approximation for area predictors. The structure of interest is an isotropic planar random compact set. The sampling device is a uniform random lattice of figures (point patterns, line segments, quadrats...). The approximation depends only on sampling parameters and on the mean perimeter (to be provided) of the structure.

Usage

 `1` ```area.mse(x, B = 1, L = 3) ```

Arguments

 `x` a lattice of figures, object of class `FigLat-class`. `B` the mean perimeter. Default: 1. `L` an integer, the criterion for stopping summation of the Epstein zeta function. Argument of the function `Ezeta`. Default: 3.

Value

The MSE approximation as a numeric.

References

Kieu, K. and Mora, M. (2006). Precision of stereological planar area predictors. J. Microsc., 222(3), 201-211.

`vol.mse`, `dvol.mse`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```# Sampling by a unit hexagonal point lattice area.mse(PPHexLat2()) # Sampling by a unit square point lattice area.mse(PPRectLat2()) # Sampling by a lattice of point patterns area.mse(PPRectLat2(n=5,hp=0.1)) # Sampling by quadrats (may be slow) ## Not run: area.mse(QRectLat2(hq=0.5,vq=0.7)) # Sampling by a square lattice of segments (may be slow) ## Not run: area.mse(SRectLat2(end=c(0.5,0.1)) # Sampling by an hexagonal lattice of segments (may be slow) ## Not run: area.mse(SHexLat2(end=c(0.2,0.15))) ```