Description Usage Arguments Details Value

Compute a MSE estimate for 3D-volume predictors. The structure of interest is a random compact set. The sampling device is a uniform random lattice of figures.

1 | ```
vol.mse.est(fldata,mse.only=TRUE,iso=FALSE,diff2use)
``` |

`fldata` |
data collected for volume prediction, object of class |

`mse.only` |
TRUE (default) if only the MSE estimate must be returned. |

`iso` |
FALSE (default) if the boundary is not assumed to be isotropic. |

`diff2use` |
a family of lattice vectors defining the data covariations to be used for the MSE estimation. A matrix with as many columns as lattice vectors. Each column contains the vector coordinates in the basis defined by the lattice generating matrix. Optional: a default value is computed. If isotropy is assumed, the lattice generating matrix (3 main basis vectors). Otherwise, 3 face diagonal lattice vectors are added to the 3 main basis vectors. |

`vol.mse.est`

invokes the function `vol.mse`

.

If mse.only is TRUE, the MSE estimate as a scalar. Otherwise a list with components:

`S.est` |
estimate of the boundary surface area. |

`deformation` |
used when the boundary is not assumed to be isotropic. It is assumed that there exists a volume preserving linear transformation which makes the boundary isotropic. This list component contains the estimated transformation matrix. |

`mse.est` |
MSE estimate. |

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