spatstat.explore (version 3.4-2)

MISE.envelope: Mean Integrated Squared Error on an Envelope Object

Description

Compute the mean integrated squared error, or integrated squared bias, or integrated variance, of the simulated function estimates in an envelope object.

Usage

ISB.envelope(object, theo, domain, dimension=2)
IV.envelope(object, domain, dimension=2)
MISE.envelope(object, theo, domain, dimension=2)

Value

A single numeric value.

Arguments

object

Object of class "envelope" generated by the function envelope

theo

Function in the R language that evaluates the true (theoretically expected) value of the spatial summary function.

domain

Numeric vector of length 2 specifying the limits of the domain of integration for the integrated squared error.

dimension

Integer (either 1 or 2) specifying whether to calculate the one-dimensional or two-dimensional integral of squared error.

Author

Adrian Baddeley , Martin Hazelton and Tilman Davies .

Details

The first argument should be an object of class "envelope" and should contain the simulated function estimates (i.e. it should have been computed using envelope with savefuns=TRUE).

MISE.envelope computes the mean integrated squared error. ISB.envelope computes the integrated squared bias. IV.envelope computes the integrated sample variance.

The simulated function estimates are extracted from object and their deviation from the true function theo is computed pointwise. The squared deviations are integrated over the interval specified by domain, giving one value of integrated squared error for each simulated function estimate. Then MISE.envelope returns the average of these values, that is, the estimated mean squared error. Similarly for the other computations.

See Also

bias.envelope, ISE.envelope.

Examples

  E <- envelope(cells, Kest, nsim=20, savefuns=TRUE)
  theoK <- function(r) { pi * r^2 }
  dom <- c(0, 0.1)
  MISE.envelope(E, theoK, dom)
  ISB.envelope(E, theoK, dom)